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Explanation of the Physical Anomalies of Water (F1-F9)

V Water has unusually high viscosity
V Large viscosity and Prandtl number increase as the temperature is lowered
V Water's viscosity decreases with pressure below 33 °C
V Large diffusion decrease as the temperature is lowered
V At low temperatures, the self-diffusion of water increases as the density and pressure increase
V The thermal diffusivity rises to a maximum at about 0.8 GPa
V Water has unusually high surface tension
V Some salts give a surface tension-concentration minimum; the Jones-Ray effect
V Some salts prevent the coalescence of small bubbles

V The molar ionic volumes of salts show maxima with respect to temperature

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

The viscosity of a liquid is the efficiency with which it flows and 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 cohesiveness 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 ˣ mol-1; D2O, 24.7 kJ ˣ mol-1; T2O, 26.2 kJ ˣ mol-1, all calculated from [73]; all at 0 °C and all more than doubling at -30 °C).  [link  Anomalies page: Back to Top to top of page]

F2    Large viscosity and Prandtl number increase as the temperature is lowered.

Dynamic viscosity, from [69], [73]

Change in dynamic viscosity with temperature; (see refs 69, 73)

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).

 

The high viscosity at low temperatures is a major cause for the very large increase in the Prandtl number (Pr).

Prandtl number = kinematic viscosity/thermal diffusivity =  specific heat x dynamic viscosity/thermal conductivity   where

ν = kinematic viscosity (m2·s-1), α = thermal diffusivity ( m2·s-1), CP = specific heat, (J·kg-1·K-1 = m2·s-2·K-1), μ = dynamic viscosity ( Pa·s = kg·m-1·s-1), k = thermal conductivity (W·m-1·K-1 = kg·m·s-3·K-1).

 

The Prandtl number, from [540]

 

The Prandt number data are from the IAPWS-95 equations [540]<

 

 

 

 

The Prandtl number is a dimensionless number that compares energy convection and conduction. Pr ≪ 1 means thermal conduction dominates over thermal convection (heat diffuses faster than matter moves; as with liquid mercury) whereas Pr ≫ 1 means that convection is more effective in transferring energy away from an area, compared to conduction; as with motor oils.

 

There is a minimum in Pr at 254.7 °C (Pr = 0.8313) [540].

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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. Water behaves anomalously below about 30 °C, at low pressures, increasing pressure reduces viscosity instead of increasing it [2891]. The viscosity passes through a pressure minimum and then increases.

 

Liquid water's pressure-viscosity behavior

 

Liquid water's pressure-viscosity behavior
Water's pressure-viscosity behavior [534, 2890] can be explained by the increased pressure (up to about 100-200 MPa) causing deformation, so reducing the strength of the hydrogen-bonded network, which is also partially responsible for the viscosity. This reduction in cohesiveness 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 close proximity of the contributing oxygen atoms [655]. Viscosity, then, increases with pressure.

 

Pressure-(relative)-viscosity behavior; from [534, 2890]

Liquid water's pressure-(relative)-viscosity behavior; data from [534] and [2890]

 

 

 

 

 

The dashed lines (above right and left) indicate the viscosity minima. Pressure can almost halve the viscosity at low temperatures. The two-state model has been used to explain the minima, with the strongly hydrogen-bonded and structured low-density water being converted to high-density water under pressure due to bending and breakage of the hydrogen bonds [2890].

 

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).

 

Diffusion versus viscosity gives two lines, from [2414]

Diffusion versus viscosity gives two lines at slightly different gradients from [2414]

 

 

Viscosity(η) and diffusion (D) are related properties through the Stokes-Einstein equation

Diffusivity=boltzman constant x temperature/(6pi x viscosity x radius) .

 

Opposite shows their Log-Log relationship with two lines switching with different exponents (ζ) close to the temperature of maximum temperature [2414].

 

 

 

 

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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 -35 °C and +100 °C. However there is a strong divergence from these Stokes-Einstein 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]; f the extensive 'sticky' low-density clusters reducing translational freedom, whereas rotational freedom is retained within the higher density intervening spaces. Below 232 K, there is a slower nucleation rate increase with decreasing temperature. probably due to an even greater reduction in water’s diffusivity [2645]. 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.

Changes in diffusivity with temperature

Changes in diffusivity with temperature

 

The activation energy for this diffusion increases to about the equivalent of two hydrogen bonds (44.4 kJ ˣ 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].

 

 

 

 

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

 

Change in diffusivity with temperature of water in nitromethane and in itself

 

Arrhenius plot of diffusivity of water

in nitromethane and in itself

 

Arrhenius plot of  diffusivity with temperature of water in nitromethane and in itself

 

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

Variation in Diffusivity of water with pressure

Variation in Diffusivity of water with pressure

Data for these tables was calculated from a the IAPWS viscosity data [540] or from [2081]. The dashed lines indicate the maxima.

 

 

Variation in Diffusivity of water with density

Variation in Diffusivity of water with density

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 4 °C, at atmospheric pressure or due to increasing pressure at low temperatures. Liquids normally show reduced self-diffusion when they are squeezed but water at 0 °C increases its diffusivity by 8% under a pressure of about 200 MPa [226] and the diffusivity of supercooled water at -30 °C increases by 60% with a similar pressure increase. The temperature limit for this anomalous behavior is ~42 °C ±5 °C in agreement with the limit of the compressibility anomaly [1970]. 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 dashed lines (above and left) indicate the diffusivity maxima.The two-state model has been used to explain the maxima, with the strongly hydrogen-bonded and structured low-density water being converted to high-density water under pressure due to bending and breakage of the hydrogen bonds [2890].

 

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 (> 200 MPa) there is an increased packing density due to the gradual phase transition to interpenetrating hydrogen-bonded networks.

 

For similar reasons involving the collapse of the hydrogen bonding, the ice surface diffusion coefficient at high pressure (10 MPa) is more than twice that observed at atmospheric pressure [1708].

 

For the same reasons, the molecular rotational movement of water (reciprocal rotational relaxation time; Debye relaxation time, τD ) also varies in direct proportion to the changes in self-diffusion (translational movement) [2890]. Thus, the rotation and translation of water are coupled [1839]. [link  Anomalies page: Back to Top to top of page]

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

Variation of thermal diffusivity with pressure

Variation of thermal difusivity with pressure

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. This is 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 and a maximum in the low-temperature thermal diffusivity - pressure behavior at about 0.8 GPa (see left, 25 °C) [614].

 

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 [1352]. [link  Anomalies page: Back to Top to top of page]

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

Surface tension explanation

Surface tension explanation

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. The surface area is known but not the volume of liquid involved.

 

Water has an abnormally high surface tension c and surface enthalpy d with an abnormally tightly packed surface compared to bulk liquid water. e Using a dynamic system, the complex surface tension of water σ* = 0.073 + i(0.017
± 0.002) N ˣ m-1 at room temperature has been determined [2155]. 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 more-fully 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 high surface tension controls drop formation in clouds and rain.

 

The surface tension and surface enthalpy behavior of liquid water

 

The surface tension/temperature (blue) and surface enthalpy/temperature (red) 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-H2O-2014.pdf Data for supercooled water from ref [865]

There is no clear anomaly in the surface tension/temperature behavior [IAPWS] above the deeply supercooled regime. There were inflection points reported at about +4 °C [865] and 256 °C [2142], (262 °C [427]), but recently the low-temperature inflection point that had been explained by use of a two-state mixture model involving low-density and higher density water clusters [866], has not been found using the capillary elevation method [2142] or a counter-pressure capillary rise method [2632]. There is, however a significant positive deviation from the extrapolated surface tension behavior below 235 K consistent with the tail of an exponential growth in surface tension as temperature decreases [2737]. This is thought due to support the coexistence of two liquid forms in pure water of macroscopic size at these low temperatures.

 

The surface enthalpy/ temperature behavior is anomalous, however, with a clear minimum at the temperature of maximum density. a This is a consequence of the minimum in the surface entropy/ temperature behavior. An interesting, if usually ignored, phenomenon is the linear reduction of surface tension with increasing relative humidity; ~0.1% drop per 1% increase in humidity at 5 °C [1854].

 

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

 

The greater than expected drop in surface tension with temperature increase (0.155 mJ ˣ m-2 ˣ 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 [376]. The thermodynamic change in surface tension with pressure is very high at 25 °C [1280]. e

 

It is interesting to note that surfactants lower the surface tension because they prefer to sit within the surface layer, 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). Many organic molecules, both hydrophilic (ethanol) and hydrophobic (neopentane), prefer the surface of the water to its bulk [1889].

 

Water strider

Water strider secretes wax onto its legs; Attribution: Markus Gayda
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 nonlinear friction effects. High surface tension is responsible for many biological effects including the ease with which water produces lingering clouds of small droplets (aerosols) that can spread pathogens widely from sneezes and high flush toilets [2259].

 

From the data on charged droplets [2660], surface charge gives rise to a large reduction in surface tension.

 

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. Similar material is known as 'dry water', behaving as a dry powder but releasing ~95%-98% liquid water on a mechanical action such as rubbing on the skin in cosmetics [1660]. This 'dry water' powder is able to efficiently take up and hold large amounts of CO2 as its clathrate (~25% CO2 by weight) [1929]. [link  Anomalies page: Back to Top to top of page]

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

Change in surface tension with concentration, from [674a]

% change in surface tension with concentration, from ref.  [674a]

There is a shallow minimum in the surface tension of many ions at very low ionic concentrations (known as the Jones-Ray effect [674]; first dismissed erroneously as an artifact by Irving Langmuir [1518]). For example, at low concentration (< 1 mM) the surface tension of KCl solutions drops (~-0.01% change) with increasing concentration. A decreasing surface tension usually corresponds to a surface enhancement, whereas an increasing surface tension corresponds to a surface deficit of the material. However in this case, the drop in surface tension has been attributed to a bulk effect rather than a surface effect [2550]. At such low concentrations, the decrease in Δγ does not stem from the surface segregation of the bare ions, but rather from the relative stability of the weakly oriented water that surrounds the bulk ions. An increase in the orientational order of the water hydrogen-bond network entails an entropic penalty that is greater in the bulk than at the surface, leading to a net favorable interaction with the surface and, hence, to a decrease in Δγ.

 

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 Sum frequency generation vibrational spectroscopy (SFG) data suggesting that these ions interact with the outermost interfacial water molecules to weaken their average water dipole moment and decrease their Gibbs free energy and thereby reduce the surface tension [2250].

 

Surface tension changes with ions, from [2396]

Surface tension changes with acid and salt concentrations, from [2396]

The supposed preference of H3O+ for the surface in some acid solutions (presumed due to its likely surface active nature, as its O atom is not hydrogen-bonded) is indicated by the slight drop in surface tension with high HCl, HNO3, and HClO4 acid concentrations (see right, [2396]). However, the anion is important as the same effect is not shown by H2SO4; thus the H3O+ ions in H2SO4 solutions show no preference for the surface. Also, NH4OH (but not NH4Cl or NaOH) shows a much more marked reduction in surface tension with concentration than these acids, which by a similar, if possibly an equally erroneous argument, might indicate a greater preference of hydroxide ion for the surface. h The surface active nature of these acids and bases is more easily and more consistently explained by the formation of uncharged species (for example, HCl, NH3) at the surface, coincident with their volatility (HCl forms 10% ion-pairs [2654]). Since writing this, the effect has been confirmed for HCl and HNO3 [2190].

 

The drop in surface tension with surface active acids is easily explainable due to greater entropy at the surface and hence lower surface energy as given by the Gibbs adsorption equation: -dγ = Σiii) where dγ is surface tension change, Γ (capital Gamma) is the surface excess of component i, and μ is the chemical potential of component i.

 

The slight rise in surface tension with salts is less easy to understand but is thought due to the relative depletion of salt within the surface, which means that when such ions do absorb near the surface a depletion layer closer to the surface must also be created. Also, higher concentrations of such salts must disproportionately increase the attractive forces on the surface water molecules, consequently adding to the increase in the surface tension. This has been further explained by the salts being at a lower concentration nearer the outside due (1) to their need for hydration on all sides, and hence residence away from the outside surface, and (2) their 'image charges' repelling them from the surface [2397]. Although the outside surface of the water is apparently no different from 'pure' water, it must be more organized (lower entropy) due to the salt organized hydration water just under this surface and thus causing the rise in surface energy (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 [1885]. This partitioning is noticeable in NaCl solutions, such as seawater; the weakly chaotropic Cl- occupying surface sites whereas the weakly kosmotropic Na+ only resides further from the surface [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 ionic surface tension increments, ki = dγ/dci (mN m-1 M-1) have been tabulated [1981] for higher molar concentrations.

pH adjusted with HCl or NaOH at 25 C, from [2073]

pH adjusted with HCl or NaOH at 25 C, from [2073]

 

Interestingly the surface tension of pure (no CO2) water shows little change with pH over the range of pH 1 - 13 on adjusting with just HCl or NaOH, except for a small local minimum around pH 4, which has been attributed as a probable manifestation of the Jones-Ray effect [2073]. The constancy of the surface tension indicates that the surface is saturated by OH- ions above pH 4 and by H3O+ between pH 0 and 3 such that bulk concentration changes have no effect.

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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 (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 (freshwater). The salts do not directly follow the Hofmeister effects (that are primarily described in terms of the individual cations or anions) with both the anion and cation having importance together 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. The reduction in this surface is preferred when it gives rise to an increase in the (closer) interactions between the oppositely charged ions.

 

Effect of ions on coalescence of small bubbles, from [1657]

 

Effect of ions on coalescence of small bubbles; from Henry and Craig (2010) ref: 1657

 

It has recently been proposed that anions and cations may be divided into two groups α and β with α cations (Na+, K+, Mg2+, NH4+) and α anions (OH-, F-, Cl-, Br-, SO42-) avoiding the surface and β anions (ClO4-, CH3CO2-, SCN-) 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 [1657]. i Bubble coalescence is inhibited when a bulk solvated or a surface active ion-pair is present in solution (αα or ββ, respectively), creating an effectively uncharged interface [1657].

 

This property of salt water enables a method for desalinating seawater [2186]. A high surface area of many tiny bubbles can be produced in a bubble column evaporator (using a sintered glass gas entry) using seawater, but not in fresh water as then the bubbles coalesce. This allows the rapid production of water-saturated air that can then be condensed.

 

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. [link  Anomalies page: Back to Top to top of page]

F10    The molar ionic volumes of salts show maxima with respect to temperature.

Molar ionic volumes of some salts

Molar ionic volumes of some salts, with temperature

The molar ionic volumes of salts, at infinite dilution, depend on both the positive intrinsic volume of the ions and the negative volume change of the water due to the ion's electric field pulling on their neighboring water molecules. Their behavior with respect to temperature is thus mostly derived from how they are able to disrupt the structuring in water (i.e. contract ithe clustering). Shown opposite is the behavior of two ionic kosmotropes, SO42- (intrinsic volume 52.94 cm3 ˣ mol-1) and Mg2+ (intrinsic volume 1.62 cm3 ˣ mol-1) and two ionic chaotropes, ClO4- (intrinsic volume 60.15 cm3 ˣ mol-1) and Cs+ (intrinsic volume 21.38 cm3 ˣ mol-1) [1599, 1912].

Volume loss when 4 g of NaOH is added to 96 g

pure water; from [2750]

Volume loss when 4 g of NaOH is added to 96 g  pure water; [2750]

 

They all are able to hold water increasingly strongly (relative to water holding water itself) at higher temperatures (where water-water hydrogen bonding is more disrupted) and as the temperature is lowered at low temperatures (where the salt interacts with the clathrate clustering.

 

The effect also causes a shrinkage in the volume that changes with temperature (see left, [2750).

 

Additionally, kosmotropes and chaotropes behave differently with the chaotropes' molar volumes changing less with temperature and reaching their maxima at higher temperatures [1599, 1912].

 

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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 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 is proportional to density [614]). [Back]

 

c A freshly exposed surface of water would be expected to have a much higher surface energy (~0.180 J m-2 [1255] ), with the surface tension reducing as hydroxide ions build up at the water-air interface [1905]. [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 ˣ m-2) ˣ (1/6.022 ˣ 1023 mol molecule-1) ˣ 1/3 ˣ (45 kJ ˣ mol-1) = ~0.125 J ˣ m-2 (compare with the actual value of 0.118 J ˣ m-2 at 25 °C). [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 ˣ m-2 ˣ MPa-1 for water at 25 °C). 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, = 0.696 nm at 25 °C) is generally much 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 3.984 °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 an 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 gases, such as CO2 (-7.7 mJ ˣ m-2 ˣ MPa-1) , than nonpolar gases such as N2 and O2 (-0.8 mJ ˣ m-2 ˣ MPa-1). [Back]

 

f A similar effect occurs in kosmotropic salt solutions such as MgCl2. As the concentration of salt increases the glass transition temperature increases as does the disparity between the rotational and translational diffusivities. With the rotational diffusivity almost independent of the viscosity, this involves a breakdown of the Stokes-Einstein relationship [1451]. This is explained, in a manner similar to the explanation for the effect in deeply supercooled pure water, as sticky clusters (here, hydrated salt ions) constantly jamming into each other (thus high viscosity) but with intervening space where water molecules can rotate unimpeded. [Back]

 

g The surface enthalpy/temperature curve was calculated from a combination of sixth power fits four ranges of surface tension data, given in [865] and [IAPWS]; and assuming the effect of changes in pressure on the change in surface tension with temperature was insignificant. Due to noise in the data and the lack of data below 250 K, the form of the curve at very low temperatures is error-prone. [Back]

 

h It has been proposed that the lesser hydration energy of OH-, relative to H3O+, results in OH- preferring the surface over the H3O+ [1025], 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]. This phenomenon, even if correct, cannot be the whole story as ions with even lower hydration energy do not seem to readily replace hydroxide ions at the interface [1505]. [Back]

 

i Originally, it was proposed that β anions (ClO4-, CH3CO2-, SCN-) avoided the surface and α anions (OH-, Cl-, SO42-) were attracted to the interface [1305] and there is still some confusion over this theory [2650]. [Back]

 

 

 

 

 

 

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