close

Вход

Забыли?

вход по аккаунту

?

Supercritical Water as a Solvent.

код для вставкиСкачать
Reviews
H. Weingrtner and E. U. Franck
Thermodynamics
Supercritical Water as a Solvent
Hermann Weingrtner* and Ernst Ulrich Franck
Keywords:
aqueous solutions · solvent properties ·
supercritical fluids · thermophysical properties · water
Angewandte
Chemie
2672
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
DOI: 10.1002/anie.200462468
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
Water is not restricted to moderate temperatures and low pressures,
but can exist up to very high temperatures, far above its critical point at
647 K. In this supercritical regime, water can be gradually compressed
from gas-like to liquid-like densities. The resulting dense supercritical
states have extraordinary properties which can be tuned by temperature and pressure, and form the basis for innovative technologies.
This Review covers the current knowledge of the major properties of
supercritical water and its solutions with nonpolar, polar, and ionic
compounds, and of the underlying molecular processes.
1. Introduction
Water, in many respects, shows unique properties that are
well characterized at ordinary conditions. Water can also
exist, and has been investigated, at states far above its critical
temperature of 647 K, where it can be gradually compressed
from gas-like to liquid-like densities. The resulting dense
supercritical states possess remarkable properties which differ
largely from those at normal conditions.[1, 2] Adopting a term
from geochemistry, such supercritical, aqueous systems are
often denoted as hydrothermal fluids.
Investigations of density variations are the key to understanding fluid behavior because such experiments allow the
temperature dependence of the fluid properties to be
separated from their volume dependence.[2] To achieve
substantial density variations, pressures up to several hundred
MPa are required. For example, for water at 773 K, a pressure
of 1 GPa is needed to generate the ordinary liquid density of
1 g cm3. Under such conditions it is likely that water will
corrode the vessels. Experiments must therefore contend with
conditions of high temperature, high pressure, and high water
corrosivity.
Under the conditions of interest, the molecular and
electronic structures of most substances are not appreciably
deformed, however, hydrogen bonds are highly sensitive to
temperature and pressure. For example, the increase in the
electrical conductance of fluid water at high temperatures and
pressures indicates a transition from molecular to ionic
states.[3, 4] Moreover, it has long been suggested that by
strong compression, the double-well potential of the hydrogen bond should degenerate into a single-well potential.[5]
Recently, a high-pressure phase of ice with symmetrical
hydrogen bonds has indeed been discovered.[6]
In many chemical and engineering applications supercritical water acts as a solvent or working fluid.[1] For example,
in steam power plants, the liquid phase may extend up to
more than 600 K, and superheated vapor can reach temperatures up to more than 900 K. Other applications include, gas
and oil recovery, hydrothermal crystal growth, and hightemperature electrochemistry.[1] The exceptional properties
of supercritical water also form major motives for searching
for industrial utilization of it as an ecologically benign solvent
in chemical reactions.[7] By tuning temperature and pressure,
states can be achieved in which water becomes completely
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
From the Contents
1. Introduction
2673
2. Supercritical Water
2674
3. Aqueous Mixtures with
Nonpolar Compounds
2680
4. Aqueous Solutions of
Electrolytes
2685
5. Conclusions
2689
miscible with nonpolar compounds, while polar and ionic
compounds remain highly soluble as well. In addition, the
viscosity remains low, even at liquid-like densities, which
enhances mass transfer and diffusion-controlled chemical
reactions. There are many interesting reactions, such as the
oxidation, pyrolysis, and hydrolysis of organic compounds,
where supercritical water acts as a solvent or reactant or
catalyst.[7]
Perhaps the most fascinating application is the destructive
oxidation of organic waste in the supercritical water oxidation
(SCWO) process.[8] At some conditions, organic waste, for
example polychlorinated biphenyl compounds, is highly
miscible with water. In the presence of oxygen, such
compounds react to carbon dioxide, water, and some other
small molecules. By careful choice of temperature and
pressure, partial oxidation of organic molecules, for example
of methane to methanol, can be achieved as well.[9] Because
the dielectric constant increases with water density, high
pressure favors the formation of polar over nonpolar oxidation products.
A phenomenon with considerable prospects is the production of combustion flames in a supercritical environment.
Figure 1 shows a “hydrothermal” flame burning in a homogenous mixture of water and methane to which oxygen is
injected from a nozzle.[8a] In this aqueous environment,
spontaneous flame ignition occurs at 673 K, markedly below
that of gaseous oxygen and methane mixtures. Such flames
can burn for 30 min or even longer, and have been spectroscopically investigated[10] and modeled.[11]
Another field of major interest is geochemistry,[12, 13]
where supercritical water acts as a solvent for hydrothermal
reactions, such as mineral formation, deposition, or dissolu-
[*] Prof. Dr. H. Weingrtner
Physikalische Chemie II
Ruhr-Universitt Bochum
44780 Bochum (Germany)
Fax: (+ 49) 234-321-4293
E-mail: hermann.weingaertner@ruhr-uni-bochum.de
Prof. Dr. Dr. h.c. E. U. Franck+
Institut fr Physikalische Chemie
Universitt Karlsruhe
76128 Karlsruhe (Germany)
[+] Deceased
DOI: 10.1002/anie.200462468
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2673
Reviews
H. Weingrtner and E. U. Franck
to extreme conditions of temperature and pressure, increase
the experimental accuracy, and provide access to bulk and
molecular properties previously not available. Theory and
computer simulations greatly improve the understanding of
these properties at the molecular level.
This Review covers these developments which are at the
root of modern supercritical water technologies. To keep the
Review manageable, we primarily focus on dense states with
high solute concentrations, such as encountered in many
chemical reactions in nature, the laboratory, and applications.
In the literature, the main emphasis is on dilute aqueous
solutions at moderate densities around 0.3 g cm3 which is
near the critical point of pure water.[1] The solvent properties
of dense supercritical water were first reviewed in 1961,[15]
when the field was in its very infancy. The latter review may
be consulted for the historical background.
Figure 1. “Hydrothermal” flame, burning in a homogeneous supercritical aqueous mixture of 70 mol % water and 30 mol % methane at
100 MPa pressure and 713 K environmental temperature, observed
through the sapphire windows of a high-pressure vessel.[8a] Oxygen is
injected from below through a nozzle at a rate of 3 mm3 s1. The
height of the flame is about 3 mm. The “gas funnel” around and
above the flame shows the upward flow of reaction products at higher
temperatures and lower density, which generate a Schlieren contrast.
There is no phase separation.
tion in the Earths mantle. Water also participates in the
formation of methane and heavier hydrocarbons of natural
petroleum. Pressure increases in the Earths mantle by about
1 GPa for every 30 km of depth, so geothermal brines
typically have pressures above 100 MPa and temperatures
above 500 K. Water at even more extreme conditions is
present in the outer planets Neptune and Uranus, which
contain a thick layer of “hot ices” between the outer
atmosphere and the core.[14] In the laboratory, such conditions
were mimicked in shock waves to pressures 180 GPa and
10 000 K,[3] where the water density is 4 g cm3, that is, four
times the normal liquid density.
In recent years, there has been great progress in the
characterization of the properties of supercritical water and
aqueous solutions, and the number of applications has rapidly
increased. New experimental techniques now push the limits
2. Supercritical Water
2.1. Phase Diagram
Figure 2 shows the phase diagram of water in the temperature–density (T,1) plane. Isobars indicate the pressures. At
Figure 2. Temperature–density diagram of water with isobars.[23, 24]
Solid circles mark breaks in the melting line which arise from to phase
transitions between the ice polymorphs. TP indicates the S–L–G triple
point at 273.15 K. CP indicates the L–G critical point.
Ernst Ulrich Franck was born in 1920 in
Hamburg. He received his doctoral degree in
1950 for work performed in the group of A.
Eucken in Gttingen about transport phenomena in gases. Initiated by this work, and
in contact with mineralogists at the University of Gttingen, above all with C. W. Correns, he established his research subject, the
study of supercritical fluids. After his “Habilitation” in 1956 he spent a research fellowship at Oak Ridge. In 1961 he was
appointed to the chair of Physical Chemistry
at the University of Karlsruhe, where he
stayed until his retirement in 1988, interrupted by many visiting fellowships. He received many scientific awards and was a member of several scientific academies. Ernst Ulrich Franck died on December 21, 2004, an
obituary was published in ref [121].
2674
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.angewandte.org
Hermann Weingrtner was born in 1948 in
Offenburg. He received his doctorate in
1976 for work carried out in the group of
H. G. Hertz in Karlsruhe on nuclear magnetic resonance in electrolyte solutions. After
his “Habilitation” in 1986 and after several
research fellowships, among others at the
Australian National University in Canberra,
he was appointed, in 1995, to a professorship for Physical Chemistry at the Ruhr-University of Bochum. His major scientific activities are in the field of thermophysical properties and phase transitions of fluids.
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
298 K, liquid water with a density of 0.997 g cm3 coexists with
water vapor with a density of 2 105 g cm3. With increasing
temperature, the density of the liquid decreases and that of
the vapor increases. At the critical point both phases become
identical and the dividing meniscus disappears. The critical
temperature (Tc), pressure (Pc), and density (1c) are:[16]Tc =
647.1 K, Pc = 22.1 MPa, 1c = 0.322 g cm3. Applications typically use range from the critical density to liquid-like densities
of about 1 g cm3.
The fluid range is encompassed by the melting line.
Breaks in the melting line indicate transitions between several
solid polymorphs of ice. Starting from the solid–liquid–gas (S–
L–G) triple point at 273.15 K, where conventional ice Ih is
stable, the melting line initially decreases (S, L, and G denote
the solid, liquid, and gaseous phases, respectively). At 251 K
and 220 MPa a new phase of ice (ice III) occurs, and the
melting line turns to higher temperatures. There follow other
polymorphs, the ices IV, V, and VI, until at 354.8 K and
2.17 GPa ice VII is formed. Ice VII is the only experimentally
observed polymorph at equilibrium with supercritical water.
The observation of such high-pressure, high-temperature
phase transitions is highly difficult. Great experimental
progress has been achieved by the development of diamond
anvil cells.[17] As schematically sketched in Figure 3, a small
Figure 3. Schematic representation of the diamond anvil cell. The sample (S) in the gasket (G) is compressed by the flat-polished opposite
faces of two diamonds.
amount of sample is held in a metal gasket between the flatpolished faces of two diamonds. The small volume of the
sample enables very high pressures to be generated. Diamonds are transparent in the optical regime, thus allowing
visual observation of the phase transitions. They are also
transparent in many other spectral regions that are exploited
by spectroscopic and scattering experiments. The pressure is
usually determined by changes in the fluorescence spectrum
of an added ruby. Recently, Loubeyre and co-workers[18] have
exploited such techniques to monitor the course of the
melting line of ice VII towards high temperatures. At the
highest temperature reached, 751.5 K, the melting pressure is
13.1 GPa. Current data collections, such as the widely used
Steam Tables,[19] still quote melting pressures obtained in from
earlier work,[20] which, in part, are almost twice as high as
those observed by Loubeyre and co-workers.
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
The continuation of the melting line to higher temperatures is of great interest in the geochemical sciences, but
extrapolations are speculative because new solid phases (ice
modifications) might occur. To some extent, experimentally
inaccessible states of water can be explored by molecular
dynamics (MD) simulations, in particular, if quantummechanical (ab initio) approaches are used. Ab initio MD
simulations[21] indeed predict a further solid polymorph at
coexistence with fluid water. In this “superionic” phase the
proton jumps between the two equivalent positions along the
O–O axis. By such simulations, the melting line was considered up to conditions in the interior of Neptune, and
suggested that regime of “hot ices” in Neptunes interior is
fluid rather than solid.[21]
2.2. P,V,T Behavior
Accurate pressure (P), volume (V), and temperature (T)
data are not only of interest in itself, but also form a
prerequisite for other studies because experiments are usually
performed at given pressure and temperature, while they are
easier understood as a function of volume and temperature.
At moderate pressure, P,V,T data can be measured by static
experiments, in which water is introduced into a pressure
vessel, and the volume of water is determined at given
temperature and pressure. Many years ago, Burnham et al.[22]
and Franck and co-workers[23] pushed such experiments to
1273 K and 1 GPa, which forms the experimental limit of such
techniques. It is believed that the uncertainties in the density
values measured does not exceed 0.5 %, but as P,V,T data
enter into many analyses of other data, such a high accuracy is
mandatory.
P,V,T data beyond these limits were derived from dynamic
experiments using shock-wave techniques. Denoting the state
prior to release of the shock wave by index “0”, shocked states
obey the Hugoniot relation for the internal energy U
[Eq. (1)].
UU 0 ¼ ðPP0 ÞðVV 0 Þ=2
ð1Þ
Thermodynamic assumptions can be used to transcribe
the measured U,P,V data into P,V,T data. More accurate
temperature measurements can be made from the emission
spectrum of the probe as determined by pyrometry. In this
way, Nellis and co-workers determined P,V,T data up to
80 GPa and 5200 K.[24]
The regime between the static and dynamic data, typically
between 1 and 10 GPa, is of great interest in geochemistry.
Efforts are currently being made to bridge this gap by new
experimental techniques. Diamond anvil cells are suited to
generate these pressures, but do not provide direct volume
information. Recently, P,V,T data up to 5 GPa and 673 K[25]
could, however, be deduced indirectly from measurements of
the speed of sound. Another remarkable method uses
synthetic fluid inclusions, which are hydrothermally generated in healing fractures of quartz or corundum. After
quenching to low temperature, the inclusions retain the
properties of the fluid before trapping. By this technique,
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2675
Reviews
H. Weingrtner and E. U. Franck
P,V,T data have been determined to 1873 K and 8 GPa.[26]
There remain discrepancies among these various data sets, so
that the P,V,T relation above 1 GPa is still uncertain.
The P,V,T relations of ammonia[30] (Tc = 461 K) and hydrogen
fluoride[31] (Tc = 406 K) have been recently reported to high
pressures and temperatures, but no detailed comparison has
been made that could single out possible peculiarities of
water.
2.3. Equations of State
The P,V,T surface of fluids is usually described by a
pressure-explicit thermal equation of state P(V,T). An
appropriate theory would predict phase equilibria, P,V,T
behavior, and other thermodynamic properties in the homogenous regime from a few physically significant input
parameters. At present, no molecular-based equation of
state fits these criteria.
In principle, simulations by Monte Carlo (MC) and
molecular dynamics (MD) techniques can provide molecular-based equations of state, but are not yet accurate enough
for applications. Moreover, there are considerable difficulties
in simulations of supercritical water, because the success of
simulations largely relies on the knowledge the intermolecular interaction potentials.[27] For water, a large number of
model potentials have been suggested and parameterized
with regard to properties at ordinary conditions. The parameterization depends however on temperature and pressure,
and the experience gained at ordinary conditions cannot
easily be transferred to supercritical states.[27] Moreover, in
some cases, the subtleties of hydrogen-bonding may require
ab initio MD simulations.[21]
Formulations of P,V,T behavior suited for applications
rely on empirical or semi-empirical approaches, often with a
large number of regressed parameters. The very properties
that make supercritical fluids so useful, that is, the transition
from gas-like to liquid-like behavior, render modeling efforts
to be difficult. Because of their simplicity many workers
prefer semi-empirical, “cubic” equations, which usually form
descendents of the popular equations of van der Waals or
Redlich and Kwong.[28] In addition, such cubic equations
usually involve parameters of some physical significance,
which facilitates data extrapolations. Many equations along
these lines have been proposed for fluids in general,[1, 28] but
are often difficult to apply for supercritical water. For
example, at very high pressures water remains much more
compressible than can be captured by the typical repulsive
terms in semi-empirical equations.[29] In addition, the nonanalytical nature of some properties discussed in Section 2.4
largely complicates the design of accurate equations of state
near critical points.
Increasing computer power now allows more general
approaches, which comprise all kinds of thermodynamic data
in a single equation for the Helmholtz energy A(T,V) as a
function of temperature and volume. Thermodynamic properties, including the P,V,T relation, then follow from partial
derivatives of A(T,V). The “International Association for the
Properties of Water and Steam” (IAPWS), which coordinates
research on thermophysical properties of water, recommends
for accurate calculations an empirical equation by Wagner
and Pruss[16] (“IAPWS-95”) valid to 1273 K and 1 GPa.
It would be interesting to compare the equations of state
for other simple hydrogen-bonded fluids with that of water.
2676
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2.4. Critical Anomalies
Near liquid–gas (L–G) critical points some properties
show divergences which obey asymptotic scaling laws of the
form of Equation (2) where t = j TTc j /Tc defines the
temperature difference from the critical point, X0 is a
system-specific amplitude, and m is a universal critical
exponent.[32]
X ¼ X 0 t m þ . . . as T ! T c
ð2Þ
Analytical equations of state can be expanded in a Taylor
series everywhere, including the critical point, and by such
expansions at the critical point the critical exponents of the
various properties X turn out to be integers or rational
fractions. For example, the L–G coexistence curve in Figure 2
obeys a scaling law of the form of Equation (3) where the socalled order parameter D1 is given by the difference of the
densities of the liquid (1L) and gaseous (1G) phases. Any
analytical equation of state provides an exponent b = 1/2,
which implies a parabolic coexistence curve.
D1 ¼ 1L 1G ¼ B0 t b þ . . .
ð3Þ
Analytical theories are denoted as “classical” or “meanfield equations. The term ”mean-field“ accounts for the fact
that, in molecular theories, analytical expressions are
obtained by assuming that the interaction of a particle with
its neighbors can be represented by the mean field generated
by its neighbors.
Experiments, however, provide critical exponents that do
not conform to the mean-field values, they give irrational
exponents and have a non-analytical behavior.[32] Instead, the
critical behavior at the L–G transition can be by described the
three-dimensional Ising spin 1/2 model.[33] This model was
originally developed for describing the interactions of spins
leading to ferromagnetic transitions. It considers the nextnearest neighbors of a particle only and presumes short-range
interactions, typically with a r6 separation dependence.
Renormalization group theory allows the exact values for
critical exponents to be computed.[33] The predicted value of
the Ising exponent, b = 0.326…, is confirmed by accurate data
for L–G transitions in fluids. Among other things, this
behavior implies that near the L–G critical point the
coexistence curve in Figure 2 is approximately cubic, and
much flatter than the parabolic shape predicted by analytical
theories.
In the mean time, there is a widespread recognition that
these anomalies give rise to considerable deficits in the
traditional equations of state. In the best case the anomalies
occur only close to Tc. These “weak anomalies” are indeed of
little significance in chemical processes, and it is not crucial
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
for applications to use a physically correct representation of
the critical divergences. In the worst case the non-classical
behavior extends over a wide temperature range. A prominent example for such a “strong anomaly” is the isobaric heat
capacity CP which goes to infinity at the critical point. About
30 K above Tc, the isothermal density dependence of CP still
shows a very pronounced maximum with a CP value that is by
an order of magnitude larger than that extrapolated from data
taken far away from the critical point.[16, 19] Even fully
empirical equations, such as the IAPWS-95 equation mentioned earlier[16] include some non-analytical terms to obtain
accurate descriptions of this behavior. In applications, the
regime of large variations is difficult to control, and is usually
avoided.
From the theoretical perspective, the anomalous phenomena close to Tc are now well understood. Large difficulties
arise, however, from the need to account for the transition
from asymptotic Ising-like behavior near critical points to
mean-field behavior expected to prevail far away. This
crossover forms the major reason for the large number of
adjustable terms needed in accurate equations of state of the
traditional form.[32] The need for a proper description of
crossover has given rise to intense experimental and theoretical efforts. Sophisticated parametric crossover theories for
fluids are now available,[32] and have been applied to water.[34]
“Parametric” means that a physically plausible crossover
function with a few adjustable parameters is used to
interpolate between the mean-field and Ising limits. In
comparison with fully empirical approaches with a large
number of parameters, crossover theories are of similar
precision, but are more difficult to implement and require
more computer time. It is likely that the future increase in
computer power will, however, favor crossover theories also
with regard to applications.
2.5. Autodissociation
A key property in many applications is the dissociation
equilibrium H2OQH+ + OH , which is characterized by the
equilibrium constant K [Eq. (4)] or the ion product KW
[Eq. (5)], where a refers to the activities of the species. At
normal conditions, ion concentrations are sufficiently low to
replace the activities by concentrations. Equations (4) and (5)
are usually formulated with H3O+ rather than H+, but at
supercritical states such a formulation is by no means
straightforward.
K¼
aðHþ ÞaðOH Þ
aðH2 OÞ
KW ¼ aðHþ ÞaðOH Þ
ð4Þ
ð5Þ
Because charged species are involved, the ion product can
be studied by electrochemical methods, such as electrical
conductance measurements. More than thirty years ago,
Holzapfel and Franck[4] performed such measurements to
1273 K and 1 GPa. Later, shock-wave experiments pushed
this limit to 180 GPa and 10 000 K.[3] Figure 4 shows the
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Figure 4. The ion product, KW, of water up to temperatures of 1273 K
and densities up to 1.5 g cm3.[35]
temperature- and density-dependence of the ion product,
derived from the ion product tables of Marshall and
Franck.[35] At normal conditions, KW = 1 1014, and the
proton concentration possesses the familiar value of 1 107 mol L1. KW increases with temperature and density. At
1273 K and liquid-like density, KW is at least six orders of
magnitude larger than at 298 K. This situation has dramatic
consequences for hydrolysis and acid–base equilibria. For
example, at 773 K and 200 MPa the equilibrium constant of
the hydrolysis reaction Cl + H2OQHCl + OH is by about
nine orders of magnitude larger than at normal conditions,
and the hydrolysis of alkali halides is comparable to that of
acetates at normal conditions. Thus, corrosion will be greatly
enhanced.
The increase in ionization is corroborated by recent
shock-wave experiments to 180 GPa and 10 000 K.[3] Near
1000 K and densities of about 2 g cm3 the conductivity begins
to level off a value of about 30 S cm1, which is comparable to
that of molten hydroxides. Raman spectra of shock-compressed water indeed show the stretch vibration of the OH
ion, but remarkably, no band for H3O+ is found.[36] The lack of
a H3O+ band gives rise to the suspicion that the cation is
H+.[36] It has been noted[37] that these highly conducting states
are of relevance for the interpretation of the large magnetic
fields of the outer planets. At the high-temperature end of the
shock-wave experiments, one may even be close to metallization of water, although no evidence for electronic
contributions to the conductance was found.[3] Ab initio MD
simulations locate the closure of the band gap at 7000 K near
300 GPa inside the fluid region.[21]
2.6. Transport Coefficients
Because all transport coefficients strongly depend on the
viscosity of the medium, an accurate knowledge of the
viscosity of supercritical water is mandatory. Figure 5 shows
experimental data for the viscosity, h, to 823 K and
350 MPa.[38] The diagram is supplemented by low-pressure
data[19] and by plausible extrapolations to 1273 K. Projected
on the floor of the cube is the liquid–gas coexistence curve
which indicates the two-phase regime.
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2677
Reviews
H. Weingrtner and E. U. Franck
Figure 5. The viscosity, h, of water at temperatures up to 1273 K and
densities up to 1 g cm3, constructed from experimental data to 823 K
and 350 MPa,[38] in conjunction with plausible high-temperature extrapolations, and supplemented by low-pressure data.[19] The coexistence
curve and critical point (CP) are shown at the floor of the cube.
tions of solute diffusion. In the dilute gas limit, D is
proportional to the ratio h/1 of the viscosity and density,
which differs drastically from the diffusion–viscosity relationship in dense phases.
In applications, mutual diffusion, often simply termed
“diffusion”, is of far greater importance than self diffusion.
The mutual diffusion coefficient, D12, describes mass flows
driven by gradients in concentrations in mixtures, as described
by Ficks laws. At the critical point, D12 goes to zero, which is
known as “critical slowing-down”. In the only study of mutual
diffusion for supercritical aqueous mixtures so far conducted,
Buelow and co-workers have demonstrated that critical
slowing-down in concentrated solutions of NaNO3 extends
over a comparatively wide region.[43] Thus, diffusion-controlled reactions in concentrated solutions may be markedly
slower than usually presumed. It can, however, be rigorously
shown that critical slowing-down must disappear at infinite
dilution of the solute. Therefore, in dilute solutions this
phenomenon can probably be ignored.
2.7. Dielectric Properties
At normal conditions the viscosities of gases and liquids
differ by about two orders of magnitude. With increasing
temperature at constant density, h increases slightly at gaslike densities and decreases markedly at liquid-like densities.
The low-density behavior reflects translational momentum
transfer and is well described by the kinetic theory of gases. In
the high-density regime collisional momentum transfer prevails, which is not yet understood in detail. There is a wide
range of densities, between 0.6 and 0.9 g cm3, where h
depends only weakly on temperature and density. In this
range, h amounts only to about one tenth of its value at
normal conditions. This high fluidity is attractive in chemical
processes because mass transfer and diffusion-controlled
chemical reactions are largely enhanced.
The low viscosity reflects high molecular mobilities. The
mean-square displacement < r2 > of a particle during time t is
described by the self-diffusion coefficient D = < r2 > /6 t. At
normal conditions Dffi2.3 109 m2 s1, at 973 K and liquidlike density Dffi108 m2 s1.[39] A similar enhancement of
molecular motions is found by nuclear magnetic[40] and
dielectric[41] relaxation techniques which probe molecular
rotations. Correspondingly, the thermal conductivity is
high,[19, 42] and thus exothermal chemical reactions can be
controlled more easily.
In dense states a hydrodynamic approach is known to
work quite well. Thus, the self-diffusion coefficient of a
particle of effective radius r obeys the Stokes–Einstein
relation [Eq. (6) where kB is the Boltzmann constant].
D¼
kB T
6 phr
ð6Þ
Equation (6) does not only apply to the self-diffusion of
water, but also to the diffusion of traces of solutes in water. At
decreasing water density, Equation (6) holds at least down to
the critical density.[39] Thus, over a large range of conditions
the factor Dh/T is almost constant, which facilitates predic-
2678
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
The relative dielectric permittivity (“dielectric constant”),
e, of water controls the solvent behavior and the ionic
dissociation of salts. Accurate experimental data for e over
large regions of temperature and pressure are therefore
necessary for many applications. Figure 6 shows the dielectric
Figure 6. The dielectric constant, e, of water up to 1273 K and densities up to 1 g cm3, constructed from experimental data to 823 K and
500 MPa,[44] in conjunction with high-temperature extrapolations based
on model calculations to 1273 K.[45] The coexistence curve and critical
point (CP) are shown at the floor of the cube.
constant to 1273 K and 1 g cm3, based on experimental data
to 823 K and 500 MPa[44] and model calculations for higher
temperatures.[45] e decreases with increasing temperature and
increases with increasing density. The familiar high value of
effi80 occurs only in a small region at low temperatures. In a
large supercritical region at high densities, the dielectric
constant has values of the order of e = 10–25. These values are
similar to those of dipolar liquids, such as acetonitrile or
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
acetone under ordinary conditions. These values are sufficiently high to dissolve and ionize electrolytes, but also enable
miscibility with nonpolar solutes. At low densities the
dielectric constant, and thus the ability to dissolve and
ionize electrolytes, decreases rapidly. At the critical point
effi6.[44]
The high values of e at normal conditions result from
preferred dipole orientations in the water structure. In
molecular theory, non-random dipole orientations are described by the Kirkwood factor gK, which in modern
formulation is related to e by Equation (7),[46] where N/V is
the number density of the dipoles, m the dipole moment of the
isolated molecule, e¥ the high-frequency limit as a result of
nuclear and electronic displacement polarizations. e0 is the
permittivity of free space; gK-values different from unity
indicate preferred parallel (gK > 1) or antiparallel (gK < 1)
dipole orientations.
ðee1 Þð2 e þ e1 Þ
m2 gK
¼
9 e0 kT
eðe1 þ 2Þ2
N
V
ð7Þ
With regard to applications there is need for an accurate
formulation that represents the dielectric constant over wide
ranges of temperature and pressure,[47] which should be
suitable for some extrapolation beyond the underlying range
of experimental data. It has long been suggested that models
for the Kirkwood factor may be simpler than for the dielectric
constant itself.[15] Irrespective of the well-defined molecular
meaning of gK, all accurate data correlations of e over wide
ranges of pressure and temperature are, however, empirical.
Some frequently used data correlations result, however, in
quite different high-temperature and high-pressure extrapolations.[48] Because at high temperatures water looses its
peculiarities, it may be more fruitful to exploit some solvable
models of statistical mechanics as a guide for extrapolation.
An attempt based on expressions for dipolar hard spheres
seems promising.[45]
From the scientific perspective, the Kirkwood factor and
the dielectric constant form useful targets for testing theories
and simulations. Moreover, gK may form a global measure of
the water structure.[49] A physically significant computation of
gK through Equation (7), is however, a subtle problem.[50]
Moreover, ab initio simulations suggest that the electric
field induced by surrounding particles enhances the dipole
moment of a hydrogen-bonded molecule, so that m increases
from the dilute gas to dense water.[51]
2.8. Hydrogen Bonding and Water Structure
At ordinary conditions the structure of water is dominated
by a three-dimensional network of hydrogen bonds. It is a
central question of any molecular approach to what extent
these hydrogen-bonded structural patterns survive in the
supercritical fluid. At the very outset, any such discussion
requires a criterion for deciding when two neighboring
molecules can be described as being hydrogen bonded. In
simulations, hydrogen bonds are usually defined by energetic
or structural properties of the molecular pair. ExperimenAngew. Chem. Int. Ed. 2005, 44, 2672 – 2692
talists resort to operational definitions, such as frequency
shifts in spectra. The various criteria can lead to largely
different estimates of the number of hydrogen bonds.[27]
In vibrational spectroscopy, hydrogen bonding leads to
frequency shifts, changes in band contours, and the appearance of new bands. Infrared spectra to 823 K and 400 MPa
were reported more than thirty years ago,[52] and were later
supplemented by Raman data.[53] Figure 7 shows Raman
Figure 7. Isotropic Raman spectra of the OD symmetric stretch vibration of 4.85 mol % D2O in H2O.[53] S is the spectral intensity in arbitrary
units, ñ is the wavenumber.
spectra of the OD symmetric stretch vibration of a solution
of 5 mol % D2O in H2O. Deuterated samples are preferred
because the OD antisymmetric and symmetric stretch
frequencies are far apart, while the OH frequencies almost
coincide. The possible hydrogen-bonded states give rise to
complex multimodal spectra with overlapping component
bands. Thus, spectral analyses is usually based on models. A
major feature observed in going at liquid-like density from
298 K to 673 K, is that the band at 2450 cm1 is gradually
replaced by a band at 2650 cm1. If at 673 K the density is
lowered, the band at 2650 cm1 shifts to higher frequencies
and approaches the limiting frequency of 2727 cm1 of the
highly dilute gas. Irrespective of details of data evaluation, it
is clear that in dense supercritical water, at least at the
temperatures considered, hydrogen bonding is retained to an
appreciable extent.
Another long established measure of hydrogen bonding is
the chemical shift of the OH proton in the 1H NMR spectrum,
but only in 1997 were such data reported for supercritical
water.[54] In contrast to vibrational spectroscopy, the longer
time scale of the NMR experiments only provides an average
degree of hydrogen bonding over the various configurations.
The results of NMR and vibrational spectroscopy are
consistent with one another.
Information on the water structure, and thus on hydrogen
bonding, is also expected from scattering techniques. Neutron
scattering is particularly suitable because, by using isotopically substituted samples, the distribution function of the
intermolecular oxygen–hydrogen separation can be extracted.
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2679
Reviews
H. Weingrtner and E. U. Franck
Difficult corrections and sophisticated numerical procedures
are, however, required to evaluate the O–H-separation
distribution functions from the raw scattering patterns.
Thus, the interpretation of neutron scattering results for
supercritical water has been controversial. A detailed discussion is given in a review by Chialvo and Cummings.[27]
Herein we note only that, in contrast to earlier claims,[55]
neutron scattering confirms the presence of hydrogen-bonded
configurations in dense supercritical states.[56] While the
experimental knowledge of the detailed water structure in
the supercritical region is still far from being complete, the
interplay between experiment and simulation has now singled
out the major structural motifs.[27]
In summary, there is no doubt that hydrogen bonds are
still present in dense supercritical water. This situation clearly
reflects the fact that at the critical temperature the energy of
the hydrogen-bond is still markedly larger than the thermal
energy. The hydrogen-bonded configurations probably consists of dimers and small clusters.[27] The properties of water
clusters are theoretically understood in great detail.[57] The
extended network structure that is responsible for the unique
properties of liquid water is, however, lost. It remains to
exploit this knowledge in terms of models for thermophysical
properties.
3. Aqueous Mixtures with Nonpolar Compounds
3.1. General Topologies of Phase Diagrams
As a rule of thumb, water is a good solvent for electrolytes
and hydrophilic substances, while it shows low solubilities for
nonpolar substances. This behavior depends, however, on
temperature and pressure. In the supercritical regime the
solubility can be tuned by density, and thus by pressure, which
opens many possibilities for using supercritical water as a
solvent and reaction medium.
When a solute is added to water, the L–G critical point is
displaced, giving rise to a locus of L–G critical points, the socalled critical curve. In addition, liquid–liquid (L–L) phase
equilibria may occur and interfere with the L–G critical
regime. For a full description of this broad variety of phase
behavior a three-dimensional pressure–temperature–molefraction (P,T,x) diagram must be used. The composition is, for
example, given in terms of the mole fraction x of one of the
components. Often one resorts, however, to the projection of
this diagram onto the P,T plane. A theory of Konynenburg
and Scott[58] suggests six types of phase diagrams in the P,T
projection. Albeit derived from an analysis of the simple
van der Waals equation for mixtures, this topological scheme
can also be applied to phase transitions in aqueous systems.[59]
Three types of phase diagram of particular interest for
supercritical aqueous solutions are depicted in Figure 8.
In the simplest cases, liquid–liquid immiscibility does not
exist or does not extend into the gas–liquid critical region. In
this sort of system, the vapor-pressure curves of the pure
liquids are terminated by L–G critical points, which are
connected by a continuous L–G critical curve for the
mixtures. If the components are completely miscible at all
2680
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 8. P,T projection of type I, II, and III phase behavior of the
Scott–Konynenburg classification.[58, 59] The projection shows the L–G
critical curve (c), vapor-pressure curves of the pure components (b), and L-L-G three-phase line (g). CP indicates the critical
points of the pure fluids. CE is the critical end point.
conditions then the phase diagram is of type I shown in
Figure 8. This type of behavior occurs for component
molecules of similar shape and polarity. Examples are
aqueous solutions of ammonia[60] and polar organic solutes,
such as ethanol or acetone.[61]
For larger dissimilarities of the components L–L equilibria develop. These miscibility gaps are well-known phenomena in aqueous solutions of organic solutes. They result
primarily from the hydrophobic nature of the solutes, which
renders mixing with water entropically unfavorable.
Schneider and collaborators have studied many L–L immiscibilities and their interference with L–G transitions,[62]
recently also in diamond anvil cells to 2 GPa or higher.[63]
For moderate hydrophobicity of the solute, the miscibility
gaps are limited to low temperatures. In this case, the phase
diagram has to account for the resulting L–L–G three-phase
line, along which two liquid phases and the gaseous phase are
in equilibrium. Additionally, there are one or more critical
curves that describe the pressure dependence of the upper
and/or lower temperatures of L–L demixing. In Figure 8 this
behavior is exemplified for a so-called type II system.
Actually, the possible phase behavior is much richer than
shown.[59, 62]
Most systems have, however, a disrupted critical curve.
This interruption is crucial for understanding solubilities in
supercritical water. In the following we presume that water is
the less-volatile component of the binary mixture, as for
example, encountered with inorganic gases and simple hydrocarbons. Then, in Figure 8 the water critical point is that at
high pressure and high temperature. The reverse case, when
water is the more-volatile component, for example, in
mixtures with salts or minerals, will be discussed in Section 4.1.
Critical-curve interruption results from the fact that an
increasing dissimilarity of the components displaces the L–L
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
equilibria to higher temperatures. Eventually, the L–L–G
three-phase line merges into the L–G critical line, and the
type II phase diagram is transferred into other types, of which
only type III behavior in Figure 8 is of relevance here.
Aqueous mixtures with nonpolar inorganic gases and simple
hydrocarbons are important examples of type III systems.
In the type III phase diagram, a L–G critical curve starts
from the critical point of the volatile nonpolar component.
Because of the low solubility of water in nonpolar fluids at
low pressure, this branch of the critical curve is, however,
rapidly interrupted by the L–L–G three-phase line at a socalled critical end point. This regime of traces of water in the
nonpolar fluid at low pressures is scarcely of interest for
applications. Rather, we focus on the high-pressure branch of
the critical curve, whose origin is in the critical point of water.
This branch runs either directly to higher temperatures and
pressures, or more often, it moves initially towards lower
temperatures and then passes a minimum. In both cases,
phase separations occur in some regions even above the
critical temperature of pure water. Because above the critical
temperature, the fluid is loosely denoted as a gas, this
behavior is sometimes denoted as “gas–gas (G–G) equilibrium”.[59] This notion is somewhat misleading because the
coexisting phases possess liquid-like densities.
Figure 9 shows a section of the P,T,x diagram for type III
systems near the critical point of water, and includes isobars
and isotherms. The shaded regime indicates the two-phase
regions of isobaric segments. The heterogeneous regime
rapidly broadens at lower temperatures, so that eventually,
nonpolar solutes are soluble in water only in trace amounts,
and vice versa. The critical curve connects the maxima of the
isotherms and the isobars forming a border, to the hightemperature side of which, is a region of complete miscibility.
Figure 9. Schematic pressure–temperature–composition diagram with
isotherms and isobars of a system composed of volatile nonpolar substances and water in the vicinity of the critical point of pure water. x(H2O) is the mole fraction of water. The shaded area indicates the twophase regime. The critical curve (a) connects the maxima of the isotherms and isobars, respectively, and limits the two-phase regime at
high temperatures. The vapor-pressure curve of pure water (d) is
also shown which ends at the critical point CP.
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
3.2. Solubility of Nonpolar Solutes
The solubility of nonpolar, nonreacting inorganic and
organic gases in water has often been studied by so-called
synthetic or analytical techniques. In synthetic experiments, a
mixture of known composition is introduced into the autoclave, and temperature and pressure are varied systematically.
In simple cases the phase transition is observed visually. More
generally, it manifests itself, for example, in breaks in P,T
curves. The synthetic method gives not only P,T,x data, but
can also be used to obtain volumetric data in the homogenous
regime, thus providing the equation of state. In the analytical
method, samples of the coexisting phases are extracted from
the autoclave and their composition is analyzed. The analytical method is particularly useful in the range of low gas
concentrations, but gives no volumetric data.
A variety of autoclaves have been devised for recording
high-pressure, high-temperature phase equilibria. Figure 10
shows an autoclave[64] that enables both synthetic and
Figure 10. Autoclave for synthetic and analytical observation of highpressure, high-temperature phase equilibria.[64] The autoclave (A) of 30cm length, 6-cm outer diameter, and 2-cm internal diameter is made
from a corrosion-resistant nickel alloy. There are three independent
heating jackets (H) controlled by three thermo couples (T). Samples
can be drawn through the connection (C) with a stainless steel capillary (SC) and a micrometric needle valve (not shown). The same connection (C) is used for filling, pressure transduction, and pressure measurement. The sample is magnetically stirred (not shown).
analytical experiments. The cylindrical autoclave (A) is
made from a corrosion-resistant nickel alloy. On both ends,
windows of synthetic sapphires (S) are mounted, which
enable observation of the interior. On the outside there are
several independent heat jackets (H). Temperature is controlled by three thermocouples (T). A thin stainless steel
capillary (SC) enables extraction of samples through a needle
valve. The same connection (C) is used for filling of the
autoclave, pressure transduction, and pressure measurement.
Figure 11 shows experimental critical curves for aqueous
solutions of representative nonpolar inorganic and organic
solutes. The hatched lines indicate the side where the systems
form two phases. At the high-temperature side the compounds are completely miscible. It is likely that these curves
are terminated at very high pressures by solid–fluid equilibria.
There is manifold interest in these critical curves in diverse
field of applications. From the industrial perspective, such
curves are of key importance as border lines, beyond which
chemical reactions can be conducted in homogeneous phases
with high concentrations of the reactants. The miscibility with
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2681
Reviews
H. Weingrtner and E. U. Franck
been reviewed by Tdheide.[13] Some discrepancies in the
reported critical curves have been cured in more recent work
by Mather and Franck.[70] CO2 is miscible with water in all
portions at temperatures more than 100 K below the critical
temperature of pure water. There have been speculations that
this enhanced miscibility reflects associated species, such as
H2CO3, and their stepwise dissociation. The thermodynamic
behavior as well as spectroscopic and conductimetric experiments give no evidence for such associated species.[13, 73]
Rather, the strong quadrupole moment of CO2 seems to
form the key for rationalizing its high solubility.
3.3. Critical Anomalies
There is much interest in nonclassical thermodynamic
behavior. Critical anomalies do not only prevail at L–G
transitions, but also apply to L–L equilibria. With regard to
the study of critical anomalies it is, of course, easier to conduct
experiments at L–L demixing (consolute) points, which often
occur near room temperature.[59]
The scaling laws for pure liquids hold in an analogous
form for liquid mixtures. In particular, for an L–L coexistence
curve, Equation (3) can be reformulated as Equation (8)
where the order parameter DF is now given by the difference
in composition of the coexisting phases.
Figure 11. P,T projection of the critical curves for aqueous solutions of
simple inorganic and organic solutes in the vicinity of the critical point
of pure water. The dashed sides of the curves indicate the side of the
two-phase regions. The line near the bottom left (b) represents the
vapor-pressure curve of pure water which terminates in the critical
point (CP). Data sources are given in the text.
solutes such as methane or carbon dioxide is of great
importance in geochemistry.
With increasing attractive interactions between the components, the shapes of the critical curves change in a regular
fashion. For the small, hard solute helium[65] the critical curve
begins from the critical point of pure water with a positive
slope. Hydrogen, a small and hard quadrupolar molecule, is
accommodated in water with little change in the critical
temperature.[66] For oxygen and nitrogen weak temperature
minima develop, which in the large-scale plot of Figure 11
practically coincide.[64] At 298 K the solubility of oxygen is
twice that of nitrogen, but this selectivity is lost at high
temperatures. For stronger interactions, the minima become
more pronounced, as observed for the higher rare gases,[67]
and exemplified in Figure 11 for some lower homologues of
the n-alkane series.[68, 69] CO2[70] and benzene[71] have strong
quadrupole moments, and the homogenous range becomes
large. Eventually, for highly polar solutes the critical curve is
not interrupted. Notably, the limiting slopes of the critical
curves at the critical point of water play a key role in the
thermodynamics of highly dilute supercritical solutions.[72]
Figure 11 shows, however, that the linear segments are small
and not relevant for most applications considered herein.
With regard to hydrothermal solutions, the behavior of
CO2 is of particular interest. Early work on CO2 + H2O has
2682
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
DF ¼ F0 F00 ¼ Bt b þ . . .
ð8Þ
The choice of the composition variable is a subtle
problem, but there are good arguments that the difference
DF1 = F’F’’ of the volume fractions of the solute in the two
phases is the most decisive quantity.[32, 74] An analysis of L–L
coexistence curves of binary mixtures shows Ising-like
behavior with the same exponent bffi0.326,[74] as found for
L–G equilibria of pure fluids. This is but one example for the
principle of isomorphism of the critical anomalies of pure
fluids and mixtures.
In the present context, the major importance of these
results is that large Ising-type critical anomalies are significant
for supercritical aqueous solutions. While some equations of
state for mixtures explicitly include asymptotic Ising behavior,[75] crossover theories in analogy to that for pure water are
lacking.[34] Even if the nature of the crossover in mixtures
would be elucidated in detail, the formulation of such a global
equation of state as a function of temperature, pressure, and
composition would be an appreciable challenge. We therefore
have to rely on classical approaches, and hope that they are
flexible enough to absorb the effects of critical anomalies in
their regressed parameters.
3.4. Equations of State
Because accurate experimental data are not easily
acquired, it is desirable to have a predictive equation of
state for supercritical aqueous solutions. The need for
predictive power requires at least semi-empirical approaches
with parameters of some physical meaning. As for one-
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
component systems, a generalized formulation in terms of the
Helmholtz energy A(T,V,x) would provide the most appropriate form. In contrast, equations of state for mixtures
usually begin with pressure-explicit relations of the form
P(V,T) for the pure fluids, which are then adapted to mixtures
by introducing mixing rules.[1] The integration of these
equations then allows chemical potentials, fugacities, or
activities, to be calculated, which in turn, provide two- and
three-phase lines by applying standard thermodynamic conditions for phase coexistence.[28]
Many equations of state have been derived for supercritical fluid mixtures in general,[1] but not all are suitable for
describing aqueous solutions. Although at supercritical states
the peculiar properties of liquid water no longer play an
important role, the conditions for an appropriate equation are
stringent, because the components have very different polarities. We consider a prototypical equation[76] which provides
good descriptions of experimental phase diagrams and
volumetric properties in the homogeneous regime, and has
some predictive power.[68, 76, 77] This equation combines the
popular Carnahan–Starling term for repulsive interactions[78]
with an attractive term based on composition-dependent
virial coefficients Bx and Cx of the square-well potential
[Eq. (9)]. hx = (p/6)NAsx3 is the packing fraction, calculated
from an core diameter sx averaged over the core diameters of
the components. The diameters sij and depths eij of the squarewell potentials for the like-particle interactions (i = j) are
derived from critical data of the pure components. Parameters
for unlike-particle interactions (i ¼
6 j) are determined by
customary mixing rules: The energy parameter is estimated
from the geometric mean, e12 = x(e11e22)1/2, of the pure
component parameters, the size parameter is estimated
from the arithmetic mean, s12 = z(s11+s22)/2. For accurate
descriptions, the mixing rules are usually modified by adjustable parameters x and z, which makes them somewhat
empirical. In practice, similar values of x and z may apply for
homologous solutes. The approximations limit this equation
of state, and many similar equations, to high temperatures. No
accurate equation for aqueous solutions spans the total range
from normal to supercritical conditions.
P ¼ RT
V 3m þ V 2mhx þ V m h2xh3x
Bx
þ RT 2
V m ðV m hx Þ3
V mV m Cx =Bx
ð9Þ
Many other equations of state have been suggested. As an
interesting example, we quote a recent equation for binary
and multicomponent mixtures by Duan, Møller, and
Weare,[79] which was shown to rationalize data up to 2 GPa
and 2000 K, even for aqueous multicomponent mixtures.[80] A
particularly interesting feature is that this equation is
calibrated, among others, against data from MD simulations.
3.5. Homogeneous Supercritical Solutions
There is much interest in the bulk and molecular properties of homogenous mixtures of water with nonpolar solutes,
both with regard to applications and to the understanding of
molecular interactions between water and nonpolar solutes.
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
As noted in Section 3.2, some experimental techniques for
measuring phase-transition curves also enable the determination of volumetric properties in the homogenous regime.
Thus, many studies of phase transitions also report on the
P,V,T,x relation.
Results of volumetric experiments are usually expressed
in terms of excess molar volumes, V̄E, which reflect deviations
from additive volume behavior of the components upon
mixing at constant pressure and temperature (the bar over the
symbol denotes molar quantities). Excess molar volumes of
supercritical mixtures with nonpolar compounds are positive,
which indicates a volume expansion upon mixing. Usually
excess molar volumes decrease at high pressures.
If V̄E is known, the excess molar Gibbs energy ḠE is
obtained by integration over the pressure starting from a
known reference state [Eq. (10)].
E ðT, Pref , xÞ þ
E ðT, P, xÞ ¼ G
G
ZP
E ðT, P, xÞdP
V
ð10Þ
Pref
Partial derivatives of ḠE with respect to P, T, and x then
allow the calculation of chemical potentials, and fugacity and
activity coefficients, which control chemical equilibria and
phase behavior. Owing to large non-ideal behavior an account
of activity or fugacity coefficients in computations of chemical
equilibria or phase equilibria is indispensable, even at the
qualitative level.
In principle, such calculations do, however, not differ from
routine calculations performed at normal conditions, where a
plethora of excess Gibbs energy models is available for
modeling.[28] There are, however, some pitfalls in treating
highly dilute solutions near the critical point of pure water,
where some properties, such as the chemical potential of the
solute, show diverging behavior. This can result in counterintuitive behavior. These subtleties are a relatively new
insight, and the literature is full of misinterpretations in terms
of dramatic structural changes in supercritical aqueous
solutions, when approaching high dilution. The problems
can be cured by proper reformulation of the theory.[72]
Limiting the discussion to more concentrated solutions,
where such subtleties can be ignored, the excess Gibbs
energies of aqueous solutions of nonpolar solutes are large
and positive, as illustrated in Figure 12 for H2O + O2.[64]
Because the excess volumes are positive, this non-ideal
behavior increases with increasing pressure. In most cases
the observed values are far higher than the typical excess
Gibbs energies of binary liquid mixtures at room temperature. In conventional interpretations such strongly positive
excess Gibbs energies are attributed to strong self-aggregation and clustering of the like particles.
Spectroscopic data that could provide information on
molecular clustering are completely lacking. Some important
information comes, however, from dielectric-constant data
for aqueous solutions of benzene.[44b] At 200 MPa and 673 K,
the dielectric constant of pure water is effi20 which corresponds to that of many polar solvents at normal conditions.
Figure 13 shows that, by adding benzene, e decreases rapidly
at constant pressure. The strong asymmetric shape of the
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2683
Reviews
H. Weingrtner and E. U. Franck
3.6 Multicomponent Mixtures
Many systems of interest in chemistry, geochemistry, and
engineering contain more than two components. Because the
number of data points needed for the characterization of
multicomponent systems is largely increased, theoretical
efforts are even more profitable. Many equations of state
can be extended to multicomponent systems in a straightforward way, and in favorable cases, information on the binary
subsystems is sufficient to describe the behavior of ternary
and multicomponent systems. Illustrative examples are studies dealing with the systems H2O + N2 + C6H14,[82] H2O + N2 +
C6H14 + CO2,[82] or H2O + N2 + CH4 + CO2.[80] This success
gives confidence for predictions made on systems where
experimental data are scarce or absent. The system H2O +
H2 + O2 is an important example of interest in diverse fields,
for example, for modeling of jet propulsion. Figure 14 shows
the computed phase diagram of at 644 K.[83] The side planes of
the prism represent heterogeneous areas of the binary
subsystems H2O + H2 and H2O + O2, for which some experimental data are available. Once the parameters of the binary
subsystems are fixed, properties such as phase-transition
curves of the ternary system, corresponding to states inside
the prism, can be computed.
Figure 12. Excess molar Gibbs energies at 673 K of H2O + O2 (top)[64]
and H2O + NaOH (bottom)[108] as a function of the mole fractions of
the solutes (O2 and NaOH) at the pressures indicated in the Figure.
Figure 14. Computed pressure–composition phase diagram of the ternary system H2O + H2 + O2 at a constant temperature of 643 K. The
side planes show the two-phase regions of the binary subsystems
H2O + H2 and H2O + O2, which are fitted to experimental data.[64, 66]
Inside the prism the computed two-phase regions of the ternary mixtures are shown. (M. Neichel and E. U. Franck, unpublished results.)
Figure 13. Dependence of the static dielectric constant, e, of water +
benzene mixtures on the mole fraction of benzene at 673 K and pressures of 200 and 40 MPa. The curve for 20 MPa is extrapolated from
these data and data at additional pressures.[44b] x(C6H6) is the mole
fraction of benzene.
composition dependence is retained at lower pressures, until
at 20 MPa and 673 K the dielectric constant of pure water no
longer differs greatly from that of benzene. Goldman and
Joslin[81] used a theory based on a density expansion of the
dielectric constant to describe these data in terms of
molecular aggregation.
2684
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
A substantially different behavior is found if one of the
components is a salt. The addition of salts to supercritical
aqueous solutions leads to “salting-out” phenomena, which
are, for example, of considerable interest for mineral formation in hydrothermal fluids. Figure 15 illustrates salting-out
effects in H2O + CO2 + NaCl.[84] It shows experimental phase
boundaries for 4 and 48 mol % of CO2 in water, and their
displacement by NaCl. At 48 mol % CO2 the addition of only
6 wt % of NaCl (relative to water) extends the heterogeneous
regime by 100 K. Even larger shifts have been observed for
methane.[85] As such experiments are extremely difficult and
time-consuming, there seems to be no substitute for modeling.
There are some promising results in this direction, for
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
Figure 15. Phase-boundary curves of binary H2O + CO2 systems at
mole fractions of CO2 of 4 and 48 % (b) and their displacement by
NaCl (c).[84] The NaCl content relative to water is 6 wt %. The vaporpressure curve of pure water (a) and the initial part of the critical
curve of the H2O + NaCl (d) system near the critical point (CP) of
pure water are also shown.
example for H2O + CH4 + NaCl and H2O + CH4 + CO2 +
NaCl.[86] In principle, such modelings suffer, however, from
the lack of information on interactions between salts and
nonpolar substances. It is usually assumed that the solubility
of salts in nonpolar fluids is completely negligible.
It is clear that many interesting applications of supercritical aqueous solutions concern geochemical problems.[12, 13]
Some geologically important hydrothermal fluids contain up
to ten or more species at concentrations sufficiently high
enough to influence phase transitions and thermodynamic
properties. A fascinating example for the power of modern
experimental technologies and theoretical modelings is the
study of hydrocarbon genesis in the Earths mantle. It is a
common belief that the hydrocarbons of natural petroleum
result from biotic organic materials under the pressure of
deposited sediments. Recently, evidence has been reported
that in the high-temperature, high-pressure hydrothermal
solutions containing CaCO3 and FeO, methane can be formed
in an abiogenic pathway.[87] Scott et al.[88] have now demonstrated the formation of methane by in situ Raman spectroscopy in a diamond anvil cell at pressures between 5 and
11 GPa and temperatures between 500 K and 1500 K, a range
which includes the typical conditions found in the Earths
mantle at a depth of about 30 km. The observations were
further supported by thermodynamic calculations based on
equations of state which were modified to allow for chemical
reactions.[88] The results suggest that an abiogenic pathway
may indeed contribute to the Earths total methane budget.
The potential exists for formation of heavier hydrocarbons in
hydrothermal systems from methane as a precursor.
4. Aqueous Solutions of Electrolytes
4.1 Salt Solubility
Coulomb interactions between charged species are much
stronger and of longer range than the interactions between
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
uncharged species. Among others, these strong interactions
lead to high critical temperatures for salts which cannot be
reached by experiments. In contrast to the situation encountered with non-ionic fluids, water is then much more volatile
than the solute. Even the temperatures of the normal melting
points (S–L) and solid–liquid–gas (S–L–G) triple points of
simple salts usually exceed the critical temperature of water.
Thus, liquid–solid equilibria in supercritical water cannot be
ignored and lead to complex phase diagrams, often involving
more than one solid phase. Experiments are usually restricted
to the water-rich regime.
For many applications it suffices to know the gross phase
behavior. This behavior mainly depends on whether the
vapor-pressure curve of the saturated solution, that is, the S–
L–G three-phase line, cuts the L–G critical line (type 2) or
does not cut it (type 1).[89] In the type 2 case salts are
practically insoluble in dense supercritical water, in the
type 1 case they are soluble. Even the type 1 electrolytes
will precipitate, however, if the water density is decreased.
Thus, instead of L–L equilibria, as encountered with non-ionic
solutes, solid–liquid equilibria are now decisive for the fate of
the L–G critical curve. Table 1 classifies some important salts
according to their solubility behavior.[89] Soluble salts of
type 1 includes most alkali and alkaline-earth halides and the
hydroxides. The group of practically insoluble salts of type 2
includes, among others, the sulfates.
Table 1: Classification of salts according to their solubility behavior in
supercritical water.[89]
Type 2 (insoluble)
Type 1 (soluble)
LiF, NaF
KF, RbF, CsF
LiCl, NaCl, KCl, RbCl, CsCl
LiBr, NaBr, KBr, RbBr, CsBr
CaCl2, CaBr2, CaI2
BaCl2, BaBr2
K2CO3, Rb2CO3
K3PO4
Rb2SO4
CaF2
BaF2
Li2CO3, Na2CO3
Li3PO4, Na3PO4
Li2SO4, Na2SO4, K2SO4
MgSO4, CaSO4
The most important example of a soluble salt is NaCl.
Bischoff and Pitzer[90] have summarized the available work on
the NaCl + H2O system and have discussed its phase behavior
in detail. Today, the critical curve is known from fluid
inclusion experiments to about 1100 K, corresponding to
30 wt % of NaCl.[91] At all compositions, the three-phase line
S–L–G[92] runs sufficiently below the critical curve to avoid an
interruption. Because liquid–liquid phase equilibria are
absent as well, the critical curve of NaCl probably remains
uninterrupted up to the critical point of NaCl above 3000 K.
Rules of thumb developed for non-electrolytes predict an
interruption whenever the ratio of the critical temperatures of
the pure compounds exceeds a value of about 2–2.5.[58, 59] For
NaCl + H2O this ratio is 5. Clearly, electrolyte solutions do
not obey this rule.
As an example for an insoluble type 2 salt, Figure 16
shows the three-phase line S–L–G of MgSO4 as a function of
the salt molarity m (mol per kg of water).[93] The key for
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2685
Reviews
H. Weingrtner and E. U. Franck
L–L phase equilibria are absent, because ion hydration
stabilizes the solutions against such a decomposition.
Actually, above 559 K the system UO2SO4 + H2O separates
into two liquid phases.[95] For a long time, this demixing was
attributed to disproportionation and hydrolysis of the uranyl
ion. Today, it is known that it forms a generic feature of hightemperature aqueous solutions of multivalent ions, but is
usually suppressed by the retrograde solubilities of the
salts.[93, 96, 97]
Support for this conjecture has come from experiments
with MgSO4, which is an important constituent of natural
solutions. The analysis of thermodynamic data suggests the
appearance of an L–L equilibrium above the retrograde
three-phase line S–L–G.[93] Figure 17 shows this behavior in a
Figure 16. Three-phase line S–L–G of aqueous solutions of MgSO4 at
high temperatures (c). In the temperature range shown the retrograde solubility means that the solid regime (S) occurs above the
liquid regime (L). The liquid–liquid coexistence curve (b) is estimated from pressure-jump experiments.[98] The experimentally
observed liquid–liquid coexistence curve of UO2SO4 + H2O (a)[95] is
also shown.
understanding such phase equilibria is a negative temperature
coefficient of the salt solubility at high temperatures. The
solubility of MgSO4 increases with increasing temperature up
to about 343 K, but then decreases. This retrograde solubility
implies that some salts of high solubility at ordinary conditions become sparingly soluble in hot water, so that in the
segment of the phase diagram shown in Figure 16 the solid
regime occurs at higher temperatures than the liquid regime.
Salts such as Na2SO4 and Na2CO3 behave similarly. As a
consequence the three-phase line will intersect the L–G
critical line at a critical end point. Because at the critical end
point the salt is present only in trace amount, this point is, in
practice, indistinguishable from the critical point of pure
water.
Many studies of such phase equilibria have been initiated
by geochemists,[12, 13] but there is considerable overlap with
systems of interest in chemical or industrial applications. Low
salt solubilities form, for example, a major problem for the
industrial realizations of the SCWO process, because the salts
may plug the reactor or connecting lines.[94] Transitions along
homologous series should, however, be noted. For example,
Table 1 shows that Na2CO3 is almost insoluble in dense
supercritical water, but K2CO3 is highly soluble. Such details
may be of great importance when faced with the choice of
neutralizing an acidic feed of a reactor by NaOH or KOH. Of
course, other properties, such the higher corrosivity of
potassium salts, have to be considered as well.
4.2 Liquid–Liquid Phase Separations in Electrolyte Solutions
In principle, the possibility for critical-curve interruption
by L–L equilibria in electrolyte solutions also exists. It is,
however, a widespread belief that in electrolyte solutions such
2686
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 17. Liquid–liquid demixing and subsequent crystallization in an
aqueous solution of MgSO4 near 430 K after a pressure jump of about
0.5 GPa (generated in a gasket of 1-mm internal diameter of a diamond anvil cell). L–L demixing results in spontaneous formation of
droplets. Needles of crystals indicate crystallization over a longer time
scale.
diamond anvil cell.[98] A pressure jump near the retrograde
three-phase line S–L–G results in a spontaneous liquid–liquid
demixing, as indicated by droplet formation. Eventually, the
formation of a solid phase gives a more stable state, so that on
a longer time scale L–L demixing is followed by crystallization. The data indicate that the L–L coexistence curve is
probably located 5–15 K above the retrograde three-phase
line S–L–G. The estimated L–L coexistence curve is shown in
Figure 16, that of UO2SO4 + H2O is given for comparison.
From the applications perspective, such L–L phase
equilibria can be handled in reactors more easily than solid–
liquid equilibria. It should, however, not be overlooked that
L–L phase separation may generate very concentrated, highly
corrosive solutions. Historically, technical and corrosion
problems caused by L–L phase separation of UO2SO4 +
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
H2O were an important drawback for considering this system
as a basis for an aqueous homogenous nuclear reactor.
From the scientific perspective, the L–L coexistence
curves are of great importance for understanding electrolyte
behavior, and can serve as important targets for testing
electrolyte theories.[96, 97] Theory shows that such equilibria
are generic features of electrolyte solutions whenever the
dielectric constant of the solvent is low. Thus, the phenomenon is not limited to high-temperature water, but is also
present in non-aqueous solvents of low e under ordinary
conditions.[99] By well-known corresponding-states arguments,[97] such systems have been used to mimic properties
of supercritical aqueous solutions that are difficult to study
directly.
solutions as model systems for supercritical water systems. By
clever choice of the salt and solvent, L–L critical points can be
generated near ordinary conditions.[99] A much investigated
system of this type is tetra-n-butylammonium picrate + ndodecanol.[96, 101, 105] which has an upper critical point of 336 K.
Taking the coexistence curve as a target, it is necessary to
discriminate between the exponent b = 1/2 in the mean-field
case and b = 0.326 in the Ising case. To a good approximation,
the coexistence curve in Figure 18 is cubic in the asymptotic
range;[105] for comparison a parabolic curve is also shown.
4.3 Critical Anomalies in Ionic Fluids
Another remarkable difference between ionic and nonionic fluids concerns the near-critical behavior. It has been
noted in Section 3.3 that the behavior of binary solutions
should be isomorphous to that of pure fluids, and thus should
exhibit Ising-like behavior. According to the renormalization
group analysis,[33] Ising-like universality is a result of the shortrange nature of molecular interactions. Thus, the Ising model
applies to non-electrolyte interactions decaying with distance
as 1/r6, but not to the 1/r-dependent Coulomb potential.[100]
The long-range nature of the Coulomb interactions could
violate the critical point universality, and give rise to meanfield critical behavior. This problem provides an intriguing
challenge for theory and experiment.[100] It is also relevant for
applications[101] because the presence of mean-field behavior
would remove many difficulties encountered in modeling
non-ionic systems.
In assessing the problem, a look at the L–G critical
behavior of metals may be fruitful. Early experiments for
alkali metals suggested mean-field criticality, but more
recently, highly accurate experiments by Hensel and coworkers for alkali metals and mercury have confirmed an
Ising-like nature of the critical point.[102] A rationale is that the
electrons screen the Coulomb interactions between the ionic
cores to such an extent that they restore Ising-like behavior.[102, 103]
In electrolyte solutions, the bare Coulomb interactions
between a pair of ions are screened by the charges of the other
ions. This effect is known as Debye-shielding. It enters, for
example, into the Debye–Hckel-theory of dilute solutions,
where it is accounted for by the concept of the “ion cloud”.[104]
The problem of the effect of Debye-shielding upon critical
behavior has given rise to much recent theoretical and
experimental work; see a comprehensive review by Weingrtner and Schrer.[96] From theory, a clear picture has not
yet evolved because for sufficiently realistic models of an
ionic fluid the necessary renormalization group analysis has
not yet become feasible. Some experimental data for supercritical aqueous NaCl solutions seem to suggest mean-field
behavior.[101]
Based on corresponding-states arguments, it seems possible to exploit L–L equilibria in non-aqueous electrolyte
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Figure 18. Experimental L–L coexistence curve of the model system
tetra-n-butylammonium picrate + n-dodecanol,[105] which according to
simple corresponding-states arguments mimics the critical behavior of
L–L transitions in high-temperature aqueous electrolyte solutions. In
the asymptotic range, the experimental points show essentially cubic
behavior. The hypothetical parabolic curve of mean-field behavior is
shown by the dashed line.
From such measurements[96, 105] the issue of asymptotic
critical behavior of ionic fluids may now be regarded as
largely settled in favor of an asymptotic Ising-like critical
character as found for non-ionic fluids. Applications usually
involve states further away from critical points, where
interesting differences between ionic and non-ionic solutes
are indeed observed. Generally, crossover to mean-field
behavior seems to be much faster for ionic than for nonionic fluids.
4.4 Systems that are Continuously Miscible up to the Molten Salt
As in the case of non-ionic mixtures, there is great interest
in characterizing the properties of salt + water systems over
the complete miscibility range up to the molten salt. In
practice, it is impossible to conduct such experiments at
liquid-like densities with salts such as NaCl. At the normal
melting temperature of NaCl of 1074 K, pressures higher than
1 GPa are necessary to compress water to a liquid-like
density. Moreover, such states of high temperature and high
density would be very corrosive. The equation of state of
NaCl + H2O only extends to 873 K, 400 MPa, and 25 wt %
NaCl.[106] For NaCl a few additional fluid-inclusion data have
been reported for higher temperatures and pressures.[107]
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2687
Reviews
H. Weingrtner and E. U. Franck
Low-melting organic salts allow the transition from dilute
electrolyte solutions to molten salts to be studied at ordinary
conditions, but their solution properties are not typical for
ionic behavior.[99] Moreover, the compressibility of such
systems is too low to generate substantial density variations.
A more suitable electrolyte is NaOH, which at normal
pressure melts at 594 K. NaOH is completely miscible with
high-density supercritical water, thus offering a broad homogeneous region for investigations. Volumetric data have been
reported up to 673 K and 400 MPa.[108] In contrast to solutions
of nonpolar solutes, the excess volumes are negative, which
indicates significant volume contraction upon mixing.
The excess molar Gibbs energies ḠE of NaOH + H2O in
Figure 12 are negative, and exhibit a strongly asymmetrical
shape for the concentration dependence with a minimum in
the water-rich regime.[108] The data yield ionic activity
coefficients that differ greatly from unity at all compositions.
In modeling chemical or phase equilibria, the consideration of
activity corrections is therefore mandatory. The difference to
the positive ḠE values of nonpolar solutes is striking. The
negative values seem to reflect a dominance of ion hydration
over other interparticle interactions. More detailed interpretations are, however, difficult because molten NaOH of low
compressibility is mixed with highly compressible supercritical water.
Figure 19. Schematic representation of the molar conductance, L, of
alkali halides, strong acids, and hydroxides as a function of the density
of water and the temperature at a constant mole fraction of the salt of
approximately 2 105, which corresponds to molar concentrations of
1 mmol L1 at normal conditions. The maximum conductance is typically of the order of 1000–1500 S cm2 mol1, which is a factor of 8–10
higher than the molar conductance at normal conditions. The L–G
coexistence curve and critical point (CP) of pure water are shown at
the floor of the cube.
4.5 Electrical Properties
Since the first investigations of the electrical conductance
of supercritical solutions of KCl, HCl, and KOH up to 1273 K
and 1 GPa,[109] this subject has been of continuing interest.[110]
Almost all conductance studies refer to dilute solutions,
typically at molar concentrations of c 0.01 mol L of the salt
(referred to 298 K), which corresponds to a mole fraction of
less than 2 104. Figure 19 shows schematically the basic
features of the molar conductance L of dilute solutions of
alkali-metal salts, strong acids, and hydroxides plotted as a
function of temperature and pressure.
L is almost zero at low water densities, where neutral ions
pairs are stable. Above 0.2 g cm3 L begins to rise up to a
maximum near 0.6 g cm3, where the dielectric constant of
water is high enough to push the dissociation equilibrium
almost entirely to the side of the free ions. The decrease of L
at still higher densities reflects the increase in the viscosity of
the solutions. The maximum conductivity is an order of
magnitude higher than that at ordinary conditions. The
“Grotthus mechanism” of rapid H+ and OH ion transport
via hydrogen bonds is less efficient at high temperatures.
For NaOH, conductance measurements have been performed up to the pure molten electrolyte.[111] Figure 20 shows
an isotherm of the molar conductance at 623 K at liquid-like
total density as a function of the mole fraction of NaOH. At
dense states, water still has an appreciable dielectric constant,
and the initial segment of the conductance curve shows the
typical high values of dissociated electrolyte solutions, which
rapidly decrease with increasing salt concentration. Above
20 mol % of salt, the gradual replacement of water by NaOH
has only a limited influence, and the conductance behavior is
2688
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 20. Isotherm of the molar conductance, L, of H2O + NaOH at
623 K and a total molar concentration of 50 mol L1 as a function of
the mole fraction of NaOH.[111]
already similar to that of a molten salt. Conductance
equations for electrolyte solutions fail in describing this
conductance behavior over the complete miscibility range, as
do some familiar expressions based on an analysis of the
conductance–viscosity (“Walden”) product L h.
If the water density is lowered, ion-pairing increases. The
electrical conductance gives, however, no information on the
configuration of the ion pairs. In favorable cases, Raman
spectroscopy may provide such information, because intramolecular vibrations in molecular ions, such as NO3 , are
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
influenced by contacts with other ions and by changes in
hydration.[112] MD simulations may also contribute to the
understanding of ion equilibria.[27] A broad range of ion
configurations from contact ion pairs to solvent-separated ion
pairs is usually found, but at low dielectric constant, contact
ion pairs are preferably formed. Again, results for electrolyte
solutions in non-aqueous solvents at normal conditions may
indicate the phenomena to be expected in supercritical
water.[97]
The high electrical conductance of supercritical aqueous
solutions enables the electrolysis of water to H2 and O2. Such
an electrolysis may, among others, be interesting for in situ
generation of oxygen in oxidation processes. Experiments at
supercritical conditions were performed in solutions of NaOH
to 400 MPa and 803 K.[113] Figure 21 shows some results
obtained with gold electrodes.
of particular interest in assessing the role of heavy-metal
complexes in fields such as SCWO technology, metallurgy, or
for understanding high-temperature corrosion. Spectroscopy
in the visible (Vis) or ultraviolet (UV) range also provides a
powerful means for investigating complex formation. For
example, the hexaquo-complexes of Co2+ ions in aqueous
CoCl2 solutions at normal conditions give pink solutions,
while at 573 K and a modest pressure of 35 MPa, the blue
color of tetrahedral complexes prevails.[114] Similar changes in
coordination have been found for other transition-metal
cations by various spectroscopic methods,[112, 114] and also by
X-ray absorption fine structure (XAFS) experiments.[115]
These changes of coordination number are intriguing because
unsaturated metal centers may coordinate with organic
ligands, thereby catalyzing the degradation of these molecules
in supercritical water. It remains to be investigated whether
high-temperature catalysts of practical use for such processes
can be developed.
4.7 Equations of State
Figure 21. Electrical current density J as a function of potential U for
aqueous solutions of NaOH of molar concentration 1 mol L1 (referring to normal conditions) at 673 K (*), 573 K ( ! ), 473 K (~), 373 K
(*), and 293 K (&).[113] The results are obtained with gold electrodes at
a surface ratio of the cathode to anode of about 1:100. The pressure is
400 MPa in all cases.
At 298 K, the current-density–potential curves show a
transition from low current densities below the decomposition potential to strongly increasing current densities above
the decomposition potential. The equilibrium decomposition
potential is E0 = 1.23 V at 298 K and 0.1 MPa, but there are
overpotentials. The equilibrium decomposition potential as
well as the overpotentials decrease with increasing temperature. At high temperatures the potential curves become
almost linear. The overpotential disappears, and current
densities become very high. High temperatures reduce the
influence of activation barriers, enhance transport processes,
and reduce ion absorption at the electrodes. As a consequence, the electrodes is almost nonpolarizable above 673 K.
The current densities of up to 35 A cm2 obtained at cell
voltages of about 2 V are two orders of magnitude higher than
those obtained in industrial electrolyzers.
Under normal conditions the thermodynamics of aqueous
electrolyte solutions has been developed to a mature state,
and theories are well founded in statistical mechanics. Practically all these theories are built upon ideas developed by
Debye and Hckel in their theory of dilute electrolyte
solutions, which, among others, results in the famous limiting
law for the mean ionic activity coefficient.[104] Treatments of
concentrated solutions rely on extensions of Debye–Hckel
theory. Above all, a semi-empirical approach developed in
many studies from 1973 onwards by Pitzer and co-workers[116, 117] is now widely used. Pitzers theory combines a
Debye–Hckel approach with a virial expansion for representing specific interactions.
Neither Pitzers model nor other approaches are suited for
extension to supercritical conditions. Some essential problems
in applications are of a technical nature, and can be cured by
reformulation of the theory.[118] A more fundamental problem
is that all these approaches rely on a Debye–Hckel-type
reference system of free ions immersed in the dielectric
continuum of the solvent. A reference system based on
interactions between free ions seems to be impractical in
regions where most ions are paired. Anderko and Pitzer[119]
have therefore gone a different way, by adopting a reference
state based on dipolar hard spheres as models for ion pairs.
This concept has been successfully applied to rationalize
phase equilibria and P,V,T properties of binary and ternary
supercritical systems.[119, 120] A theory that spans the total
range from normal to supercritical conditions requires the
connection of this approach with the Debye–Hckel-type
theories. Such a global approach is not yet available.
5. Conclusions
4.6 Transition-Metal Complexes
Knowledge of the ions present in solutions of transitionmetal cations and of the stability regions of these aggregates is
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Dense supercritical water is a medium which provides an
unusual variety of interesting phenomena. Continuous
changes of thermophysical properties can be achieved by
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2689
Reviews
H. Weingrtner and E. U. Franck
pressure variation, and result in transitions from “gas-like” to
“liquid-like” behavior. With plausible extrapolations, the
existing data base is sufficient to establish an equation of state
to 1273 K and 1 GPa. From shock-wave experiments, there is
even information on some properties of water at several
thousand Kelvin and up to almost 200 GPa.
The ultimate aim is to explain macroscopic properties in
terms of molecular interactions. In this regard, the advent of
high-speed computers opens new ways. While simulations are
not yet accurate enough for practical applications, they
provide much insight into the molecular origin of the various
phenomena. In this regard, the fluid structure of water and
the underlying nature of the hydrogen bonds play a key role.
It is now ensured by many experiments and simulations that
hydrogen bonds exist in dense states far above the critical
temperature of water.
The change in the thermophysical properties of supercritical water with temperature and density has dramatic
consequences for its solvent behavior. At high-temperatures
water looses the familiar high selectivity towards polar and
ionic compounds, and in some range of temperature and
pressure nonpolar compounds become highly miscible. Typically, at 673 K, all inorganic gases and simple organic
compounds, if not destroyed, are completely miscible with
water at pressures up to several 100 MPa. At high water
densities some salts are highly soluble as well. This opens a
window for generating homogeneous aqueous solutions with
high concentrations of solutes of largely different polarity.
This extraordinary behavior is, of course, impossible at
ambient conditions, and forms the conceptual basis of
innovative techniques such as SCWO technologies. Other
interesting chemical applications can be conceived.
Because in many situations, one is fairly close to critical
points, the challenge of incorporating the nonclassical critical
nature of fluids into theories and data correlations still
remains. There is now widespread recognition that such
effects are not limited to the vicinity of the critical point, but
in some cases extend to states far away. In this regard, many
equations of state are deficient. In the best case, the critical
anomalies are implicitly absorbed in adjustable parameters of
the classical models. In the worst case, largely erroneous
predictions are obtained. While the asymptotic scaling laws
now allow an appropriate description near critical points, the
understanding of crossover to classical behavior further away
is still a challenge. A detailed understanding of this interplay
between universal critical phenomena on the one hand and
molecular interactions on the other remains a problem.
In this context it should be noted that the Coulomb
interactions in ionic systems are much stronger and of longer
range than van der Waals interactions in non-ionic fluids. This
situation gives rise to substantial changes in phase behavior
associated with the high critical temperatures and pressures
and the high melting points of the salts. While in most
supercritical solutions of nonpolar solutes phase behavior
only fluid phase equilibria occur, in supercritical electrolyte
solutions solid–fluid equilibria often play a decisive role. This
fact has major consequences for industrial applications
because salt precipitation in reactors is much more difficult
to handle than fluid coexistence. Claims that the long-range
2690
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
nature of the Coulomb interactions even violates criticalpoint universality were, however, not confirmed by recent
experiments.
As the strength of the Coulomb interactions crucially
depends on their shielding by the dielectric constant of the
solvent, a wide variety of ion configurations ranging from
complete dissociation to complete association into neutral
pairs can occur in supercritical water, which gives rise to large
difficulties in formulating equations of state for supercritical
aqueous electrolytes. For many transition metal ions, specific
complex formation has to be considered as well. Pressure
variation can lead to interesting changes in coordination
which, in the light of possible prospects for catalysis, have yet
to be explored in detail. Finally, the decisive role of supercritical solutions for geochemical processes should be emphasized again.
Received: October 29, 2004
Published online: April 13, 2004
[1] a) Steam, Water and Hydrothermal Systems: Physics and
Chemistry Meeting the Needs of Industry (Eds.: P. R. Tremaine,
P. G. Hill, D. Irish, P. V. Balakrishnan), NRC, Ottawa, 2000;
b) “Supercritical Fluids, Fandamentals and Applications”: E.
Kiran, P. G. Debenedetti, C. J. Peters, NATO Sci. Ser. Ser. E
2000, 366; c) Supercritical Fluid Technology (Eds. T. J. Bruno,
J. F. Ely), CRC, Boca Raton, FL, USA, 1991.
[2] a) E. U. Franck in ref. [1a], pp. 22–34; b) E. U. Franck in
ref. [1b], pp. 307–322. c) E. U. Franck, J. Chem. Thermodyn.
1987, 19, 225 – 242; d) E. U. Franck, H. Weingrtner in Chemical Thermodynamics. A Chemistry for the 21th Century
Monograph, (Ed. T. Letcher), Blackwell, London, 1999,
pp. 105 – 119.
[3] R. Chau, C. Mitchell, R. W. Minich, W. J. Nellis, J. Chem. Phys.
2001, 114, 1361 – 1365.
[4] W. B. Holzapfel, E. U. Franck, Ber. Bunsen-Ges. 1966, 70,
1105 – 1112.
[5] W. B. Holzapfel, J. Chem. Phys. 1972, 56, 712 – 715.
[6] a) P. Loubeyre, R. LeToullec, E. Wolanin, M. Hanfma, D.
Hauserman, Nature 1999, 397, 503 – 506; b) M. Benoit, A. H.
Romero, D. Marx, Phys. Rev. Lett. 2002, 89, 145501.
[7] a) D. Brll, C. Kaul, A. Krmer, P. Krammer, T. Richter, M.
Jung, H. Vogel, P. Zehner, Angew. Chem. 1999, 111, 3180 –
3196; Angew. Chem. Int. Ed. 1999, 38, 2998 – 3014; b) E.
Savage, Chem. Rev. 1999, 99, 603 – 622.
[8] a) W. Schilling, E. U. Franck, Ber. Bunsen-Ges. 1988, 92, 631 –
636; b) R. W. Shaw, T. B. Brill, A. A. Clifford, C. A. Eckert,
E. U. Franck, Chem. Eng. News 1991, 69, 26 – 39.
[9] T. Hirth, E. U. Franck, Ber. Bunsen-Ges. 1993, 97, 1091 – 1098.
[10] G. M. Pohsner, E. U. Franck, Ber. Bunsen-Ges. 1994, 98, 1082 –
1090.
[11] M. Sauer, F. Behrendt, E. U. Franck, Ber. Bunsen-Ges. 1993, 97,
900 – 908.
[12] See, for example, D. T. Rickard, F. E. Wickman, Chemistry and
Geochemistry of Solutions at High Temperatures and High
Pressures, Pergamon, Oxford, 1981.
[13] K. Tdheide, Ber. Bunsen-Ges. 1982, 86, 1005 – 1016.
[14] B. Hubbard, Science 1997, 275, 1279 – 1280.
[15] E. U. Franck, Angew. Chem. 1961, 73, 309 – 322.
[16] W. Wagner, A. Pruss, J. Phys. Chem. Ref. Data 2002, 31, 387 –
535.
[17] a) G. J. Piermarini, S. Bloch, Rev. Sci. Instrum. 1975, 46, 973 –
979; b) J. D. Barnett, S. Bloch, G. J. Piermarini, Rev. Sci.
Instrum. 1973, 44, 973, 1 – 9.
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Angewandte
Supercritical Water
Chemie
[18] F. Datchi, P. Loubeyre, R. LeToullec, Phys. Rev. B 2000, 61,
6535 – 6546.
[19] L. Haar, J. S. Gallagher, G. S. Kell, NBS/NRC Steam Tables:
Thermodynamic and Transport Properties and Computer Programs for Vapour and Liquid States of Water in SI-Units, US
National Bureau of Standards, Gaithersburgh, 1984.
[20] C. W. Pistorius, M. C. Pistorius, J. P. Blakey, L. J. Admiraal, J.
Chem. Phys. 1963, 38, 600 – 602.
[21] C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, M.
Bernasconi, M. Parinello, Science 1999, 283, 44 – 46.
[22] C. W. Burnham, J. R. Holloway, N. F. Davies, Am. J. Sci. A
1969, 276, 70 – 95.
[23] a) S. Maier, E. U. Franck, Ber. Bunsen-Ges. 1966, 70, 639 – 645;
b) H. Kster, E. U. Franck, Ber. Bunsen-Ges. 1969, 73, 716 –
722.
[24] G. A. Lyzenga, T. J. Ahrens, W. J. Nellis, A. J. Mitchell, J. Chem.
Phys. 1982, 76, 6282 – 6286.
[25] E. H. Abramson, J. M. Brown, Geochim. Cosmochim. Acta
2004, 68, 1827 – 1835.
[26] a) C. Withers, S. C. Kohn, R. A. Brooker, B. J. Wood, Geochim.
Cosmochim. Acta 2000, 64, 1051 – 1057; b) J. P. Brodholdt, B. J.
Wood, Geochim. Cosmochim. Acta 1994, 58, 2143 – 2148;
c) D. J. Frost, B. J. Wood, Geochim. Cosmochim. Acta 1997,
61, 3301 – 3309.
[27] A. Chialvo, P. T. Cummings, Adv. Chem. Phys. 1999, 109, 115 –
205, and references therein.
[28] See, for example, J. M. Prausnitz, R. N. Lichtenthaler, E.
Gomes de Azevedo, Molecular Thermodynamics of FluidPhase Equilibria, Prentice-Hall, Eaglewood Cliffs, 1986.
[29] K. S. Pitzer, S. M. Sterner, J. Chem. Phys. 1994, 101, 3111 – 3116.
[30] A. Harlow, G. Wiegand, E. U. Franck, Ber. Bunsen-Ges. 1997,
101, 1461 – 1465.
[31] E. U. Franck, G. Wiegand, R. Gerhardt, J. Supercrit. Fluids
1999, 15, 127 – 133.
[32] M. A. Anisimov, J. V. Sengers in Equations of State for Fluids
and Fluid Mixtures (Eds.: J. V. Sengers, R. F. Kayser, C. J.
Peters, H. J. White), Elsevier, Amsterdam, 2000.
[33] a) M. E. Fisher, Rev. Mod. Phys. 1998, 70, 653 – 681; b) “Scaling,
Universality and Renormalization Group Theory”: M. E.
Fisher, Lect. Notes Phys. 1983, 186, 1 – 119.
[34] A. K. Wyczalkowska, Kh. S. Abdulkadirova, M. A. Anisimov,
J. V. Sengers, J. Chem. Phys. 2000, 113, 4985 – 5002.
[35] W. L. Marshall, E. U. Franck J. Phys. Chem. Ref. Data, 1981, 10,
295 – 304.
[36] N. C. Holmes, W. J. Nellis, W. B. Graham, G. E. Walrafen, Phys.
Rev. Lett. 1985, 55, 2433 – 2436.
[37] W. J. Nellis, D. C. Hamilton, N. C. Holmes, H. B. Radouski,
F. H. Ree, A. C. Mitchell, M. Nicol, Science 1988, 240, 779 – 781.
[38] K. H. Dudziak, E. U. Franck, Ber. Bunsen-Ges. 1966, 70, 1120 –
1128.
[39] W. Lamb, G. A. Hoffman, J. J. Jonas, J. Chem. Phys. 1981, 74,
6875 – 6880.
[40] N. Matubayashi, N. Nakao, M. Nakahara, J. Chem. Phys. 2001,
114, 4107 – 4115.
[41] K. Okada, M. Yao, Y. Hiejima, H. Kohno, Y. Kajihara, J. Chem.
Phys. 1999, 110, 3026 – 3036.
[42] F. J. Dietz, J. J. deGroot, E. U. Franck, Ber. Bunsen-Ges. 1981,
85, 1005 – 1009.
[43] T. J. Butenhoff, M. G. E. Goemans, S. J. Buelow, J. Phys. Chem.
1996, 100, 5982 – 5992.
[44] a) K. Heger, M. Uematsu, E. U. Franck, Ber. Bunsen-Ges. 1980,
84, 758 – 762; b) R. Deul, E. U. Franck, Ber. Bunsen-Ges. 1991,
95, 847 – 853.
[45] E. U. Franck, S. Rosenzweig, M. Christophorakos, Ber. BunsenGes. 1990, 94, 199 – 203.
[46] J. G. Kirkwood, J. Chem. Phys. 1939, 7, 911 – 991.
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
[47] M. Uematsu, E. U. Franck, J. Phys. Chem. Ref. Data 1980, 9,
1291 – 1306.
[48] D. P. Fernandez, A. R. H. Goodwin, E. W. Lemmon, J. M. H.
Levelt Sengers, C. R. Williams, J. Phys. Chem. Ref. Data 1997,
26, 1125 – 1166.
[49] Y. Marcus, J. Mol. Liq. 1999, 81, 101 – 113.
[50] H. Weingrtner, J. Mol. Liq. 2002, 98–99, 293 – 301.
[51] M. Boero, K. Terakura, T. Ikeshoji, C. C. Liew, M. Parrinello,
Phys. Rev. Lett. 2000, 85, 3245 – 3248.
[52] E. U. Franck, K. H. Roth, Discuss. Faraday Soc. 1967, 43, 108 –
114.
[53] W. Kohl, H. A. Lindner, E. U. Franck, Ber. Bunsen-Ges. 1991,
95, 1586 – 1593.
[54] a) N. Matubayashi, C. Wakai, M. Nakahara, Phys. Rev. Lett.
1997, 78, 4309; b) N. Matubayashi, C. Wakai, M. Nakahara, J.
Chem. Phys. 1997, 107, 9133 – 9140; c) M. M. Hoffman, M. S.
Conradi, J. Am. Chem. Soc. 1997, 119, 3811 – 3817.
[55] R. H. Tromp, P. Postorino, G. W. Neilson, M. A. Ricci, A. K.
Soper, J. Chem. Phys. 1994, 101, 6210 – 6215.
[56] a) A. Botti, F. Bruni, M. A. Ricci, A. K. Soper, J. Chem. Phys.
1998, 109, 3180 – 3184; b) K. Soper, F. Bruni, A. K. Ricci, J.
Chem. Phys. 1997, 106, 247 – 254.
[57] R. Ludwig, Angew. Chem. 2001, 113, 1856 – 1876; Angew.
Chem. Int. Ed. 2001, 40, 1808 – 1827.
[58] P. H. Van Konynenburg, R. L. Scott, Discuss. Faraday Soc.
1970, 49, 87 – 97.
[59] R. S. Rowlinson, F. L. Swinton, Liquids and Liquid Mixtures,
Butterworths, London, 1982.
[60] D. S. Tsiklis, L. R. Linhits, N. P. Goryunova, Zh. Fiz. Khim.
1965, 39, 2978 – 2981.
[61] W. L. Marshall, E. V. Jones, J. Inorg. Nucl. Chem. 1974, 36,
2319 – 2323.
[62] G. M. Schneider, Phys. Chem. Chem. Phys. 2002, 4, 845 – 852.
[63] a) R. Grzanna, G. M. Schneider, Z. Phys. Chem. 1996, 192, 41 –
47; b) H. Weingrtner, D. Klante, G. M. Schneider, J. Solution
Chem. 1999, 28, 435 – 446.
[64] M. L. Japas, E. U. Franck, Ber. Bunsen-Ges. 1985, 89, 1268 –
1275; M. L. Japas, E. U. Franck, Ber. Bunsen-Ges. 1985, 89,
793 – 800.
[65] N. G. Sretenskaya, R. J. Sadus, E. U. Franck, J. Phys. Chem.
1995, 99, 4274 – 4277.
[66] T. M. Seward, E. U. Franck, Ber. Bunsen-Ges. 1981, 85, 2 – 7.
[67] Y. S. Wei, R. J. Sadus, E. U. Franck, Fluid Phase Equilib. 1996,
123, 1 – 15.
[68] M. Neichel, E. U. Franck, J. Supercrit. Fluids 1996, 9, 69 – 74.
[69] E. Brunner, J. Chem. Thermodyn. 1990, 22, 335 – 353.
[70] A. E. Mather, E. U. Franck, J. Phys. Chem. 1992, 96, 6 – 8.
[71] Z. Alwani, G. M. Schneider, Ber. Bunsen-Ges. 1969, 73, 294 –
301.
[72] J. M. H. Levelt Sengers in ref. [1c], pp. 1–56.
[73] R. Kruse, E. U. Franck, Ber. Bunsen-Ges. 1982, 86, 1036 – 1038.
[74] S. C. Greer, M. R. Moldover, Annu. Rev. Phys. Chem. 1981, 32,
233 – 265.
[75] J. C. Rainwater in ref. [1c], pp. 58–162.
[76] M. Christoforakos, E. U. Franck, Ber. Bunsen-Ges. 1986, 90,
780 – 789.
[77] M. Heilig, E. U. Franck, Ber. Bunsen-Ges. 1989, 93, 898 – 905.
[78] N. F. Carnahan, K. E. Starling, J. Chem. Phys. 1969, 51, 635 –
636.
[79] Z. H. Duan, N. Møller, J. H. Weare, Geochim. Cosmochim.
Acta 1996, 60, 1209 – 1216.
[80] Z. H. Duan, N. Møller, J. H. Weare, Geochim. Cosmochim.
Acta 2000, 64, 1069 – 1075.
[81] S. Goldman, C. Joslin, Ber. Bunsen-Ges. 1995, 99, 204 – 210.
[82] M. Heilig, E. U. Franck, Ber. Bunsen-Ges. 1990, 94, 27 – 35.
[83] E. U. Franck, M. Neichel, unpublished results.
www.angewandte.org
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
2691
Reviews
H. Weingrtner and E. U. Franck
[84] M. Gehrig, H. Lentz, E. U. Franck, Ber. Bunsen-Ges. 1986, 90,
525 – 533.
[85] T. Krader, E. U. Franck, Ber. Bunsen-Ges. 1987, 91, 627 – 634.
[86] Z. H. Duan, N. Møller, J. H. Weare, Geochim. Cosmochim.
Acta 2003, 67, 671.
[87] J. F. Kenney, V. A. Kutcherov, N. A. Bendeliani, V. A. Alekseev, Proc. Natl. Acad. Sci. USA 2002, 99, 10 976 – 10 981.
[88] H. P. Scott, R. J. Hemley, H.-K. Mao, D. R. Herschbach, L. E.
Fried, W. M. Howard, S. Bastea, Proc. Natl. Acad. Sci. USA
2004, 101, 14 023 – 14 026.
[89] a) W. L. Marshall, Chemistry 1975, 48, 6 – 12; b) V. M.
Valyashko, Pure Appl. Chem. 1997, 69, 2271 – 2280.
[90] J. L. Bischoff, K. S. Pitzer, Am. J. Sci. 1989, 289, 217 – 248.
[91] A. L. Knight, R. J. Bodnar, Geochim. Cosmochim. Acta 1989,
53, 3 – 8.
[92] K. G. Kravchuk, K. Tdheide, Z. Phys. Chem. 1996, 193, 139 –
150.
[93] H. Weingrtner, Ber. Bunsen-Ges. 1989, 93, 1058 – 1065.
[94] M. Hodes, P. A. Marrone, G. T. Hong, K. A. Smith, J. W. Tester,
J. Supercrit. Fluids 2004, 29, 265 – 288.
[95] C. H. Secoy, J. Am. Chem. Soc. 1950, 72, 3343 – 3345.
[96] H. Weingrtner, W. Schrer, Adv. Chem. Phys. 2001, 116, 1 – 66.
[97] a) H. Weingrtner, W. Schrer, Pure Appl. Chem. 2004, 76, 19 –
27; b) H. Weingrtner, Pure Appl. Chem. 2001, 73, 1733 – 1748;
c) H. Weingrtner, W. Schrer, in ref. [1a], pp. 320–327.
[98] H. Weingrtner, unpublished results.
[99] H. Weingrtner, T. Merkel, U. Maurer, J. P. Conzen, H.
Glasbrenner, S. Kshammer, Ber. Bunsen-Ges. 1991, 95,
1579 – 1586.
[100] a) M. Fisher, J. Stat. Phys. 1994, 75, 1 – 36; b) G. Stell, J. Stat.
Phys. 1995, 78, 197 – 338.
[101] K. S. Pitzer, J. Phys. Chem. 1995, 99, 13 070 – 13 077, and
references therein.
[102] F. Hensel, J. Phys. Condens. Matter 1990, SA33 – SA45.
[103] F. Hensel, W. C. Pilgrim, Contrib. Plasma Phys. 2003, 43, 206 –
210.
2692
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
[104] a) P. Debye, E. Hckel, Phys. Z. 1923, 24, 185 – 206; b) R. A.
Robinson, R. H. Stokes, Electrolyte Solutions, Butterworths,
London, 1969.
[105] M. Kleemeier, S. Wiegand, W. Schrer, H. Weingrtner, J.
Chem. Phys. 1999, 110, 3085 – 3099.
[106] M. Gehrig, H. Lentz, E. U. Franck, Ber. Bunsen-Ges. 1983, 87,
597 – 600.
[107] R. J. Bodnar, Pure Appl. Chem. 1995, 67, 873 – 880.
[108] S. Kerschbaum, E. U. Franck, Ber. Bunsen-Ges. 1995, 99, 624 –
632.
[109] E. U. Franck, Z. Phys. Chem. 1956, 8, 92 – 106; E. U. Franck, Z.
Phys. Chem. 1956, 8, 107 – 126; E. U. Franck, Z. Phys. Chem.
1956, 8, 192 – 206.
[110] P. Ho, D. A. Palmer, M. S. Kruszkiewicz, J. Phys. Chem. B 2001,
105, 1260 – 1266, and references therein.
[111] A. Eberz, E. U. Franck, Ber. Bunsen-Ges. 1995, 99, 1091 – 1103.
[112] a) D. E. Irish, T. Jarv, Appl. Spectrosc. 1983, 37, 50 – 55; b) P. D.
Spohn, T. B. Brill, J. Phys. Chem. 1989, 93, 6224 – 6231.
[113] H. Boll, E. U. Franck, H. Weingrtner, J. Chem. Thermodyn.
2003, 35, 625 – 637.
[114] H. D. Ldemann, E. U. Franck, Ber. Bunsen-Ges. 1967, 71,
455 – 460; H. D. Ldemann, E. U. Franck, Ber. Bunsen-Ges.
1968, 72, 514 – 523.
[115] M. M. Hoffmann, J. G. Darab, B. J. Palmer, J. L. Fulton, J. Phys.
Chem. A 1999, 103, 8471 – 8482.
[116] See, for example, K. S. Pitzer in Activity Coefficients in
Electrolyte Solutions (Ed.: K. S. Pitzer), 2nd ed., CRC, Boca
Raton, 1991, pp. 75 – 153.
[117] K. S. Pitzer, J. Phys. Chem. 1973, 77, 268 – 277.
[118] J. M. H. Levelt Sengers, C. M. Everhart, G. Morrison, K. S.
Pitzer, Chem. Eng. Commun. 1986, 47, 317 – 328.
[119] A. Anderko, K. S. Pitzer, Geochim. Cosmochim. Acta 1993, 57,
1657 – 1680.
[120] Z. Duan, N. Møller, J. H. Weare, Geochim. Cosmochim. Acta
1995, 59, 2869 – 2882.
[121] F. Hensel, Angew. Chem. 2005, 117, 1180; Angew. Chem. Int.
Ed. 2005, 44, 1156.
www.angewandte.org
Angew. Chem. Int. Ed. 2005, 44, 2672 – 2692
Документ
Категория
Без категории
Просмотров
0
Размер файла
895 Кб
Теги
water, supercritical, solvents
1/--страниц
Пожаловаться на содержимое документа