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The Puzzling Properties of Supercooled and Glassy Water.

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DOI: 10.1002/anie.200601053
Water Anomalies
The Puzzling Properties of Supercooled and Glassy
Ralf Ludwig*
amorphous ice · phase transitions · polyamorphism ·
supercooled water · water anomalies
The relationship between liquid, supercooled, and glassy water is an exciting
topic of research.[1–3] The hypothesis of a
liquid–liquid critical point for water
assumes the existence of two different
liquid phases at low temperatures. These
two phases are supposed to meet at a
second critical point. However, even if
this liquid–liquid critical point exists, it
would lie in the “no-man#s-land” where
liquid water cannot be studied by direct
experimental means because the lowtemperature liquid would freeze. Recent
experimental and theoretical studies
have improved our knowledge about
supercooled and glassy water.[4–11] They
deliver further pieces for understanding
the puzzling behaviour of liquid water
and contribute towards a coherent picture of this ubiquitous substance. Despite significant progress in water research, important questions remain.
Water’s Anomalies
Water is a remarkable liquid as it
possesses a number of highly unusual
properties not displayed by other liquids. The peculiar properties of water
are a result of the hydrogen-bonding
network between the oxygen and hydrogen atoms of water molecules (Fig[*] Prof. Dr. R. Ludwig
Institut f0r Chemie
Abteilung Physikalische Chemie
Universit5t Rostock
Dr.-Lorenz-Weg 1
18051 Rostock (Germany)
Fax: (+ 49) 381-498-6524
[**] This work was supported by the Deutsche
Forschungsgemeinschaft (Forschergruppe
436, Lu506/5-3).
ure 1). Above 320 K water behaves like
a “normal” liquid. Upon heating, the
density decreases, and the thermal compressibility and the isobaric heat capacity both increase. This behavior is known
below the melting point. If these properties are extrapolated below the lowest
temperatures, they appear to become
infinite at the unreachable temperature
of Ts = 228 K. It is assumed that the
explanation of water#s anomalies can be
found in the metastable water phases.
Supercooled and Glassy water
Figure 1. Molecular structure of liquid water.
Molecules typically form hydrogen bonds
(blue bars) with four neighbors in a tetrahedral fashion. The liquid displays an open,
loosely packed, structure. The atoms of the
central water molecule and its first neighboring shell are shown as spheres.
for “normal” liquids such as liquified
noble gases, liquid metals or organic
liquids. However, upon cooling the density goes through a maximum at 277 K,
and the isothermal compressibility and
the isobaric heat capacity pass minima
at 319 K and 308 K, respectively (Figure 2).
Further cooling below these temperatures leads to a strong decrease in
density and strong increase for both the
thermal compressibility and the isobaric
heat capacity. The temperature changes
of these water properties become more
pronounced in the supercooled region
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
As mentioned above, water displays
maximum density at 277 K, only 4 K
above the melting point. Since liquid
water#s anomalies are quantitatively
small at ambient temperature, the behavior of liquid water is investigated at
lower temperatures where the anomalies become much more pronounced
(Figure 2). Normally water freezes below the melting point Tm to form
hexagonal ice Ih, which is the thermodynamically stable phase. But liquid
water can exist inside the crystalline
domain of stability. This supercooled
water represents a metastable liquid
(Figure 3).
Minor perturbations can trigger the
sudden appearance of the stable crystalline phase. If liquid water is cooled fast
enough and freezing can be avoided
altogether, then water becomes a noncrystalline solid, which is called a glass.
Glassy water can exist when the temperature drops below the glass transition
temperature Tg = 136 K. Although
glassy water is a solid, its structure
exhibits a disordered liquidlike arrangement. Initially investigators found two
amorphous ice forms: low-density amorphous ice (LDA) and high-density amorphous ice (HDA). The phenomenon
that a pure material can exist in more
than one amorphous state is called
Angew. Chem. Int. Ed. 2006, 45, 3402 – 3405
Figure 3. Temperature domains of stability
and metastability for liquid and glassy water
at atmospheric pressure. Equilibrium transitions are shown as solid lines, kinetically
controlled transitions as dotted lines. Tb denotes the boiling point, Tm the melting point,
TH the homogeneous nucleation temperature,
and Tg the glass transition temperature.
Adapted from references [1] and [3].
Figure 2. Temperature dependence of a) the
density 1, b) the coefficient of thermal expansion ap, c) isothermal compressibility kT, and
d) the constant-pressure specific heat Cp. The
anomalous thermodynamics and fluctuations
of liquid water are apparent above the melting
temperature Tm, and they become much more
striking when water is supercooled below Tm.
The temperature behavior of “normal” liquids
is given by the red lines.
polyamorphism. The two glassy states
differ in structure and in bulk properties.
Unfortunately glasses are nonequilibrium materials; their physical properties
depend on how the glassy states were
produced. A sharp and reversible transformation between different glassy
forms suggests a thermodynamic phase
transition. LDA and HDA can be interconverted by compression and decomAngew. Chem. Int. Ed. 2006, 45, 3402 – 3405
pression at temperatures below the
crystallization temperature. A sharp
change in the density of the amorphous
sample was observed when LDA was
compressed, and hence the transition to
HDA was called “first-order-like”. On
heating, LDA and HDA are thought to
undergo a glass transition resulting in
highly viscous, supercooled liquids referred to as low-density liquid (LDL)
and high-density liquid (HDL), respectively. Thus the transition between LDA
and HDA is a low-temperature manifestation of a first-order transition between the two phases of liquid water. At
higher temperatures LDL and HDL
meet at a second critical point (C2)
(Figure 4). The two liquid phases are no
longer distinguishable, like the gas and
the liquid phases above the liquid–gas
critical point (C1 at 647 K). However,
the exact connection between the different amorphous ice forms and supercooled liquid water is not clear, in
particular since the “no-man#s-land”
region largely prohibits direct experimental access.
The proposed liquid–liquid critical
point is supported experimentally by the
changing slope of the metastable melting curves observed for different ice
polymorphs[3, 12] Further support was
recently provided by Klotz et al.,[4] who
Figure 4. The most probable thermodynamic
scenario for the phase behavior of metastable
water. In keeping with the hypothesized liquid–liquid phase transition, a first-order phase
transition occurs between the LDL and HDL
forms of supercooled liquid water. The transition between the HDA and LDA forms of
amorphous ice is the low-temperature manifestation of that phase change. The physical
properties change smoothly in going from
LDL to LDA and from HDL to HDA. The firstorder transition terminates at a so-called
second critical point C2. The regular critical
point C1 terminates the liquid–gas coexistence curve. Unfortunately C2 is expected to
be between the homogeneous nucleation
curve (TH) and the crystallization curve to
cubic ice (“no-man’s-land”). This makes it
extremely difficult to observe it experimentally.
Adapted from references [1] and [3].
used neutron scattering diffraction to
study the transition between LDA and
HDA at 0.3 GPa and 130 K. A progressive transformation of one distinct phase
to another, with phase coexistence at
constant pressure and temperature,
gives direct evidence of a classical firstorder transition. Although the results
tend to support this intriguing possibility, a second critical point could not be
New Findings
The scenario of two supercooled
liquid phases has been recently questioned owing to the discovery of a third
disordered modification apparently distinct from HDA and LDA and called,
because of its higher density, very-high-
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
density amorphous ice (VHDA) ice.[13]
VHDA is generated by heating HDA
under pressure. The resulting glass does
not convert back to HDA when it is
recovered at ambient pressure at 77 K.
The relation between VHDA and HDA
phases is important to support the
hypothesis that two distinct phases of
liquid water, namely LDL and HDL,
exist below a critical temperature.
In this context two important questions arise: Which phase, HDA or
VHDA, resembles more closely liquid
water at high pressure? If there are two
different high-density amorphous ices
does this imply the existence of more
than one form of HDL?
Simulation studies indicate that
(VHDA) is a more stable form of
HDA. Thus VHDA should be considered as the amorphous ice of the
quenched liquid-water phase HDL at
ambient conditions.[5, 6] Koza et al.[7]
have demonstrated by using elastic and
inelastic neutron scattering that HDA
and VHDA are heterogeneous on the
length scale of nanometers and that
different forms of HDA are obtained,
depending on the exact preparation
process. Tulk et al. have found by annealing of HDA at normal pressure[14]
evidence for the presence of a multitude
of (metastable) amorphous ice states.
Very recently Loerting et al.[8] described a stepwise formation process
LDA!HDA!VHDA at 125 K; this is
the first observation of a stepwise transformation sequence between three
amorphous phases. The transition from
HDA to VHDA on isothermal compression at 125 K has been found to be
similar to the transition from LDA to
HDA. The authors suggest the presence
of a well-established first-order phase
transition between the HDA and
VHDA amorphous ices. It may be that
the two steps between LDA, HDA, and
VHDA are analogues in the glassy state
for phase transitions between LDL,
HDL, and VHDL, respectively. Conversions between LDA, HDA, and VHDA
suggest that densification of amorphous
ice occurs as two thermodynamically
distinct transitions. However, Loerting
et al.[8] could not exclude a kinetically
controlled densification process in
amorphous ice.
Theoretical calculations on supercooled and amorphous water suggest
that a thermodynamic transition between HDA and VHDA is possible by
showing that several metastable liquids
separated by first-order phase transitions and critical points can be found for
various water potentials. Based on computer simulations, Brovchenko et al.[9, 15]
were the first to conclude that even
more than one liquid–liquid transition
might exist in supercooled water.
As mentioned above, the search for
the predicted first-order liquid–liquid
transition line and its end point, the
second low-temperature critical point in
water, has been hampered by the intervention of homogeneous nucleation,
which takes place at 231 K at ambient
pressure. However, by confining water
in nanopores of mesoporous silica, Liu
et al.[10] were able to study the pressure
effect on the dynamic behavior of water
in the deeply supercooled state without
crystallization. They found clear evidence of a fragile-to-strong dynamic
transition. The authors related the measured transition temperature line to the
liquid–liquid transition line obtained by
molecular dynamics simulations. Above
a pressure of 1600 bar the characteristic
feature of this transition can no longer
be discerned. This end point is discussed
as possible low-temperature critical
Why is the understanding of supercooled and glassy water so important?
Three main reasons can be given: Supercooled water and amorphous metastable
water are more than just curiosities since
they do exist in many places in the real
world. Small droplets of supercooled
water exist in stratiform and cumulus
clouds. In the processing of solar and
terrestrial radiative energy fluxes supercooled water also plays a crucial role.[16]
It is also important for life at subfreezing
conditions, for the commercial preservation of proteins and cells, and for the
prevention of hydrate formation in natural-gas pipelines.[1]
Besides water, other network-forming substances also display anomalies in
their densities, isothermal compressibilities, heat capacities, diffusion coeffi-
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
cients, and kinematic viscosities. SiO2,
GeO2, Si, and Ge also form tetrahedral
networks and display at least two different amorphous states.[17] Thus studying
supercooled water and amorphous ice is
important for the fundamental understanding of the molecular requirements
for macroscopically anomalous thermodynamic behavior.
And finally, it has been shown that
water#s anomalies are more pronounced
in the supercooled region. Fluctuations
of the entropy and volume increase with
decreasing temperature. The existence
of two liquid phases, LDL and HDL,
terminating in a second critical point
could explain water#s anomalies easily.
In keeping with the hypothesized liquid–liquid critical point, the observed
water anomalies are simply the beginning of the transformation of highdensity “normal” water to low-density,
highly ordered liquid.
Despite the exciting new findings
about supercooled and glassy water, we
still cannot explain the sharp increase of
the thermodynamic properties upon
supercooling, the nature of the transitions between LDA, HDA, and VHDA,
and the relationship between supercooled and glassy water. Instead of
investigating small structural or thermodynamic changes upon water transformation it may be a good idea to study
more sensitive properties. Paschek[11]
found that the structural transformation
of water into a low-density liquid in the
supercooled range strongly enhances
the solubility of hydrophobic particles.
The transformation of water into a
tetrahedrally structured liquid is accompanied by a minimum in the hydration
entropy and enthalpy.
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2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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