”The Physics and Chemistry of Water”
6 – ’Hydrophobic’ interactions
A non-polar molecule in water disrupts the Hbond structure by forcing some water molecules
to give up their hydrogen bonds.
As a result, water near the solute will rearrange in order to minimise the number of lost Hbonds. This imposes a new structure on neighbouring water molecules, which is entropically
unfavourable.
The differences in dispersion interaction between water and e.g. hydrocarbons is rather small,
and so the size and shape of the solutes are critical in determining the change in free energy upon
dissolution.
A comment on terminology
Hydrophobic substances
– Non-polar substances with low miscibility in
water, such as hydrocarbons or fluorocarbons.
Hydrophobic surfaces
– Surfaces which are not wetted by water, and
against which water subtends a large contact angle.
The hydrophobic effect
– The immiscibility of non-polar substances in
water, and the mainly entropic nature of this incompatibility.
Hydrophobic hydration (solvation)
– The distortion of water structure in the vicinity
of non-polar solute molecules or surfaces.
Hydrophobic interaction
– An unusually strong interaction between hydrophobic molecules and surfaces in water.
Effect of temperature on the
hydrophobic effect
Free energy of transfer of pentane from the bulk liquid to
aqueous solution (from Creighton).
The strong temperature dependence of of both
∆G and ∆S is a result of the different heat capacities of the two phases. Over the whole T range
there is a large positive heat capacity change upon
transfer to water;
d∆G
d∆H
d∆S
∆Cp = −T
=
=T
dT 2
dT
dT
Some comments on the
temperature dependence
• In cold water (room temperature) the effect is
mainly due to entropy; −T ∆S À 0, ∆H ≈ 0.
• In hot water (near boiling) it is mainly enthalpic; ∆H À 0, −T ∆S ≈ 0. Although the
entropic term approaches zero, which may be
taken to suggest that water-ordering has disappeared, ∆Cp is still considerable, so much of
the ordering is still remaining. Anyhow, water
behaves much more like a normal solvent at
high temperatures.
• There are two different measures of
”maximum hydrophobicity”:
i) The free energy of transfer ∆G has a maximum where ∆S = 0.
ii) The equilibrium constant for transfer (which
is proportional to −∆G/T ) is at a maximum where ∆H = 0.
Driving forces require interpretation in terms
of free energy, while the solubility is lowest at
room temperature. Thus between 300 and 380
K the free energy becomes more positive, yet
the solubility of oil in water increases.
Effect of hydrocarbon chain length on
the hydrophobic effect
Free energy of transfer (µ◦HC − µ◦W ) of hydrocarbons from
water to liquid hydrocarbon at 25◦C (from Tanford).
Effect of hydrocarbon surface area
Free energy of transfer ∆G = ∆H − T ∆S from
bulk liquid to water.
Thermodynamics of dissolution in water at 25◦C as a function of accessible hydrocarbon surface area, dashed line: aliphatics, solid line: aromatics (from Creighton).
∆G
(kJ/mol)
Methane
14.5
n-butane
24.5
Area*
(nm2)
∼0.5
∼1.0
∆G/area
(mJ/m2)
48
41
*With a 0.2 nm van der Waals radius, the surface area/molecule
for methane is 4πa2 ≈ 0.5 nm2 , the area of n-butane is about
4πa2 + 2πa(3 × 0.1275) ≈ 1.0 nm2 .
Compare with free energies of water-hydrocarbon
interfaces, which typically are 40-50 mJ/m2.
Solubility minima for small
non-polar solutes
Solubility of liquid benzene in water, as mole fraction X2 of
dissolved solute (data from Ha et al., J. Mol. Biol. 209,
801 (1989)).
The hydration has two contributions:
a) The endothermic creation of a cavity.
b) The exothermic addition of a molecule.
At low temperatures, cavities are formed at a relatively low cost, so the solubilization is exothermic, and solubility decreases with increasing temperature (Le Chatelier’s principle).
At higher temperatures, the structure in the
liquid is less open, so creating voids in the water
becomes more difficult, the process is endothermic, and (Le Chatelier’s principle again) solubility increases with increasing temperature after
having passed a minimum.
Isotope effects
Hummer et al., Chem. Phys. 258, 349 (2000)
D2O is generally a better solute for small nonpolar solutes than H2O, despite forming stronger
H-bonds and being a more strongly associated
liquid.
Experimental relative free energy of transfer from H2O to
D2O. The dashed line is the relative change in surface tension.
The stronger H-bonds in D2O leads to a more icelike structure with a lower (number) density, with
an increased number of (small) molecule sized
cavities and thus an increased solubility.
Experimental evidence for
hydrophobic hydration I
Soper & Finney, PRL 71, 4346 (1993)
Neutron diffraction from 1:9 molar ratio methanolwater mixtures (6 different isotopic combinations,
resulting in 10 distinct partial structure factors).
Left: H–H pair correlation functions for the 1:9 MeOH/H2O
mixture (line) and for pure water (circles). Right: Pair correlation function for the MeOH and H2O molecular centers.
The peak at ∼3.7 Å indicates a shell of water around the
methanol molecules in solution.
• Water forms a loose H-bonded cage around
the methanol molecule.
• The water shell around the methanol molecules
is achieved without significant modification of
the order between water molecules.
• Results contradict speculations about enhancement of water structure by alcohols.
Experimental evidence for
hydrophobic hydration II
Bowron et al., PRL 81, 4164 (1998)
EXAFS characterization of hydrophobic hydration of Krypton in water and ice.
Kr-O partial pair-correlation function in the liquid state at
∼ 5◦, and in ice. Numbers refer to densities at the location
of the first peak.
The hydration ”cage” is more loosely defined in
the liquid, but the number of molecules in the
first coordination shells are similar; ∼13 in the
liquid and ∼12.5 in the solid.
Diffusion of atomic hydrogen (H*) I
Kirchner et al., PRL 89, 215901 (2002)
Par-Carrinello simulation of 63 H2O molecules in
a 12.6 Å cubic periodic box.
Partial pair-correlation functions (left ordinate) and running
coordination numbers (right ordinate) for an H atom (H*)
in water at 315 K.
A hydration shell is formed with H2O molecules
oriented with an H atom closer to the H* than
the oxygen. The average distance of H* from the
H2O molecules is similar to O–O-distances in the
bulk.
Diffusion of atomic hydrogen (H*) II
Kirchner et al., PRL 89, 215901 (2002)
Dynamical properties of the solvation shell.
Mean-square displacements of the H* atom, the cavity center, ”bulk” water and H* relative to the cavity center, indicating anomalously fast diffusion of H* in water.
• The cavity trajectory suggests that H2O in
the solvation shell are exchanged, as opposed
to diffusion of small cations which travel with
their hydration shell attached.
• The fast migration of the cavity appears to
be caused by rapid fluctuations in the H-bond
network, permitting rapid exchange.
• Results do not support the idea of a ”frozen”
solvation shell.
Hydrophobic interactions
• Attraction between hydrophobic molecules in
water is often stronger than their attraction in
free space; the van der Waals energy for two
contacting methane molecules is −2.5 × 10−21
J in free space, but −14 × 10−21 J in water.
• Continuum theories predict a reduced interaction in water.
• This phenomenon is the result of H-bond configurational rearrangement in two overlapping
hydration shells as they approach; it is thus
longer ranged than chemical bonds.
• Driving force for self-assembly of biological membranes, protein folding, polymer association,
micellization, etc.
Amphiphilic association
Evans & Miller, Water Science Reviews 4, 1 (1989)
Thermodynamics of micellization of C14TAB. Over
the range 25 to 160◦C, the free energy remains almost constant, while the CMC increases by a factor of 10, and the aggregation number decreases
from 72 to 8.
Interaction between a methane molecule
and a paraffin wall in liquid water
Wallqvist et al., Chem. Phys. Lett. 145, 26 (1988)
Monte Carlo simulation of 216 molecules, RWK2M (RWK2 + internal vibrations) modeling of
water-water, different LJ interactions for watermethane and wall-methane, water-wall potential
V (z) = a/z 9 − b/z 3.
Distribution functions of methane molecules relative to the
wall for the gas and solvent phase. The wall is at 11.8 Å.
The hydrophobic solute is not forced into contact
with the wall by the water, but is stabilized in a
solvent-separated configuration by the hydrogenbonded network.
General references
• A. Ben-Naim, Water and aqueous solutions, New York:
Plenum 1974.
• T. Creighton, Proteins: Structure and molecular properties, New York: Freeman (1993).
• J. N. Israelachvili, Intermolecular and surface forces,
London: Academic Press 1992.
• C. Tanford, The hydrophobic effect: Formation of micelles and biological membranes, New York: Wiley 1973.