PAPER
www.rsc.org/pccp | Physical Chemistry Chemical Physics
Diffusion coefficients and local structure in basic molten fluorides:
in situ NMR measurements and molecular dynamics simulationsw
Vincent Sarou-Kanian,a Anne-Laure Rollet,*ab Mathieu Salanne,b
Christian Simon,b Catherine Bessadaa and Paul A. Maddenc
Received 25th June 2009, Accepted 28th September 2009
First published as an Advance Article on the web 20th October 2009
DOI: 10.1039/b912532a
The local structure and the dynamics of molten LiF–KF mixtures have been studied by nuclear
magnetic resonance (NMR) and molecular dynamics simulations. We have measured and
calculated the self-diffusion coefficients of fluorine, lithium and potassium across the full
composition range around the liquidus temperature and at 1123 K. Close to the liquidus
temperature, DF, DLi and DK change with composition in a way that mimics the phase diagram
shape. At 1123 K DF, DLi and DK depend linearly on the LiF molar fraction. These results show
that the composition affects the self-diffusion of anions and cations more weakly than the
temperature. The activation energy for diffusion was also determined and its value can be
correlated with the strength of the anion–cation interaction in molten fluoride salts.
1. Introduction
Molten salts are a particular class of liquids. They differ from
the classical solvents like liquid water because of the ionic
character of all their components. On the atomic scale, the
structure is governed by the combination of coulombic and
short-range repulsion forces.1 Several families of molten salts
can be distinguished, depending on the chemical properties of
the liquid. In the case of high melting temperature systems,
these are mainly dependent on the nature of the anions,
so they are commonly named molten chlorides, fluorides,
oxides, etc.
Among these families of molten salts, molten fluorides have
a particular importance from a technological point of view
because of their potential use as solvent and coolant in several
generation IV nuclear reactor concepts.2,3 This explains the
continuous effort devoted to the study of the physico-chemical
and electrochemical properties of molten fluorides since the
early 1990s despite the substantial experimental difficulties
encountered when studying them: one has to deal with the
problems of high temperatures ranging from 500 to 1800 K,
concerning corrosiveness and volatility.
It is now well known that within the family of molten
fluorides important modifications in the thermodynamic and
transport properties occur when the nature of the cation is
changed.4,5 One can distinguish acidic cations, which tend to
a
Conditions Extreˆmes : Mate´riaux à Haute Température et
Irradiation – CNRS, 1D avenue de la Recherche Scientifique,
45071 Orle´ans cedex 2, France. E-mail: [email protected],
[email protected]; Tel: 33 2 38257682
b
UPMC univ. Paris 06, CNRS, ESPCI, UMR 7195 PECSA,
F-75005 Paris, France. E-mail: [email protected],
[email protected], [email protected]
c
Department of Materials, University of Oxford, Parks Road,
Oxford, UK OX1 3PH. E-mail: [email protected]
w Electronic supplementary information (ESI) available: Self-diffusion
coefficients versus composition in LiF–BeF2 molten salt. See DOI:
10.1039/b912532a
This journal is
c
the Owner Societies 2009
form long-lived ionic bonds with the fluoride anions6,7 from
basic ones, which provide ‘‘free’’ fluoride anions to the melt,
even though a proper scale of acidity remains to be built in
these media.8 Molten lithium fluoride (LiF) and potassium
fluoride (KF) are archetypal basic molten salts, and so are
their mixtures. The viscosity of these mixtures is known to be
of the same order of magnitude as liquid water, which means
that these liquids are highly fluidic.9 Up to now no reliable
information on the diffusion coefficients of the different species
has been available, and the objective of this work is to provide
such data for all the LiF–KF compositions, and to study their
evolution with temperature.
To achieve this objective, two independent techniques are
employed. The first is experimental, and it employs a newly
developed experimental capability.10 The diffusion coefficients
are directly measured by the high temperature pulsed field
gradients nuclear magnetic resonance experiments (HT PFG
NMR), for temperatures ranging between 750 and 1123 K.
This technique has numerous advantages: the acquisition of
data is rapid, one can select an isotope, and it does not
necessitate the use of any model to link the measured
data to the diffusion coefficient.11 These experiments were
supplemented by molecular dynamics (MD) simulations. In
this method, the system is treated on the atomic scale, and
Newton’s equation of motion is propagated for a given set of
particles, which allows for the determination of dynamic
properties. The interaction potential between the various
species is of ab initio accuracy and includes dipole polarization
effects. It has already been tested against various types of
experimental data, and is shown to reproduce accurately
quantities like electrical conductivity, heat capacity, viscosity,
etc, of different molten fluoride systems.12
In this paper, both methods will be described in the first
section. Then the data collected will be compared and discussed. A particular emphasis will be given to the composition
and temperature dependence.
Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11501
asymptotic multipole expansion of dispersion. These functions
take the form
2. Experimental and methods
2.1
NMR
The LiF and KF salts (purity 99.99%) were purchased from
Alfa Aesar. They were stored and the mixtures were prepared
in a glove box under argon in order to avoid H2O and O2
contamination of the samples. The salts were confined in
boron nitride crucibles (without oxide binder). The amount
of salt in each crucible is ca. 50 mg.
The HT PFG NMR spectra were recorded using a Bruker
Avance WB 400 MHz spectrometer, operating at 9.40 T. The
experimental setup has been described in details in another
publication.13 Nevertheless, the principle can be recalled. The
BN crucible is heated by a symmetrical irradiation of CO2
laser. Thanks to its good thermal conductivity, the crucible
acts as a small furnace. The laser power is progressively
increased to take the temperature about 101 above the liquidus
temperature. An argon stream prevents the BN from oxidizing
at high temperature. The NMR probe is a 10 mm liquid probe
especially designed by the Bruker company and adapted in
CEMHTI to work up to 1500 K. It is equipped with a gradient
coil providing 5.5/G/cm A1 that is combined with a gradient
amplifier of 10 A (Great 10A).
We used an NMR pulse sequence combining bipolar
gradient pulses and stimulated echo.14 This sequence is repeated
with 8 gradients of increasing strength. The self-diffusion
coefficients are obtained by nonlinear least-squares fitting of
the echo attenuation.
Measurements were performed using the following NMR
parameters: times of radiofrequency magnetic field application
for p/2 pulses p90 = 13 ms (19F) and p90 = 9 ms (7Li), gradient
strength 0 o g o 50 Gauss cm1, gradient application time
1 o d o 5 ms. For 7Li measurements, we used a pre-saturation
cycle before the diffusion sequence because of the long relaxation
time T1 of this nucleus (25 s in molten LiF).
The 19F chemical shifts were referred to CCl3F.
2.2
Molecular dynamics
The LiF–KF liquid mixtures have been studied by MD
simulations. In the case of molten fluorides, the potential is
best described as the sum of four different components:
charge–charge, dispersion, overlap repulsion, and polarization.15
First the charge–charge term is
V qq ðrij Þ ¼
X qi qj
ioj
ð1Þ
rij
where qi is the charge on ion i, and formal charges are used
throughout. The dispersion component includes dipole–dipole
and dipole–quadrupole terms,
V
disp
ðrij Þ ¼ X
ioj
"
C ij
f6ij ðrij Þ 66
rij
þ
Cij
f8ij ðrij Þ 88
rij
#
ð2Þ
where C6ij (C8ij) is the dipole–dipole (dipole–quadrupole)
dispersion coefficient, and fnij are Tang–Toennies dispersion
damping functions describing the short-range correction to the
11502 | Phys. Chem. Chem. Phys., 2009, 11, 11501–11506
fnij ðrij Þ ¼ 1 cijn expðbijn rij Þ
n
X
ðbij rij Þk
n
k¼0
k!
ð3Þ
and the parameter bij represents the distance at which the
correction begins to be taken into account. The third term of
the interaction potential, the repulsion overlap component, is
given by:
V rep ðrij Þ ¼
X
Aij expðaij rij Þ
ð4Þ
ioj
The polarization part of the potential includes charge–dipole
and dipole–dipole terms,
V pol ðrij Þ ¼
X
ðqi mj;a f4ij ðrij Þ qi mi;a f4ij ðrij ÞÞ Tað1Þ ðrij Þ
ioj
X
ð2Þ
mi;a mj;b Tab ðrij Þ þ
ioj
ð5Þ
X 1
jl j2
2ai i
i
Here Ta(1) and Tab(2) are the charge–dipole and dipole–dipole
interaction tensors while ai is the polarizability of ion i. Again,
Tang–Toennies functions are included to account for the
short-range effects. The set of induced dipoles li is treated as
3N additional degrees of freedom of the system. The dipoles
are determined at each time step by minimization of the
total polarization energy and depend on the positions of
all the atoms at the corresponding time; therefore the
polarization part of the potential is considered to be a many
body term.
All the parameters necessary to simulate LiF–KF mixtures
have been determined from a recently developed first-principles
procedure. The pair parameters are summarized in Table 1.
The polarizabilities were, respectively, of 7.9 and 5.0 a.u.
for F and K+ ions, while the Li+ were considered to be
non-polarizable.
The MD simulations were performed on 11 molten salt
compositions ranging from pure LiF to pure KF. All the
corresponding simulation cells contained 432 ionic pairs.
The mixtures were first equilibrated in the NPT ensemble
following the method described by Martyna et al.,16 with a
pressure fixed at 0 GPa and a temperature of 1200 K.
We chose a time step of 0.5 fs and after 100 ps of
equilibration, production runs of 200 ps were conducted for
each composition.
Table 1 Parameters of the interaction potential (in atomic units). For
all the ion pairs, b6ij = b8ij = 1.9 and c6ij = c8ij = 1.0
Ion pair ij
Aij
aij
C6ij
C8ij
b4ij
c4ij
c4ji
F–F
F–Li+
F–K+
Li+–Li+
Li+–K+
K+–K+
282.3
18.8
138.8
1.0
1.0
1.0
2.444
1.974
2.04
5.0
5.0
5.0
15.0
1.2
3.9
0.1
0.3
1.0
150.0
12.2
38.7
1.0
3.2
10.0
—
1.834
1.745
—
—
—
—
1.335
2.500
—
—
—
—
—
0.31
—
—
—
This journal is
c
the Owner Societies 2009
3. Results
3.1
Local structure
The chemical shift of 19F, 19Fd has been measured as a
function of the composition and the values are plotted in
Fig. 1.
The chemical shift is sensitive to the local environment of
the observed nucleus, i.e. the first shells of neighbours.17 For
solid compounds, the NMR spectrum yields as many peaks as
there are different environments for the observed nucleus,
if the resolution is sufficient. On the contrary, for molten salts,
the nucleus experiences all the different environments during
the measurement and NMR spectrum is made of only one
sharp peak. However, this peak is the weighted average of all
the individual peak positions that would be sampled if the
measurement was infinitely fast. Therefore the observed values
can be expressed as follows:
d=
P
nixidi
(6)
where ni is the number of fluorine involved in the ith complex,
xi the molar fraction and di its chemical shift.
In most molten fluoride mixtures 19Fd presents complicated
variations with composition. For example, in NaF–AlF3 there
are several linear variations versus AlF3 concentration.18 In
rare earth fluorides AF–LnF319,20 (Ln = La, Y, Ce, Lu and
A = Li, Na, K, Rb) and actinide fluorides21 AF–ThF4 the
variation is a parabola. In these two cases, it has been
demonstrated that fluoride ions are in rapid exchange between
at least three environments: free fluorine, fluorine embedded in
long-lived LnFx3x unit22 and fluorine bridging two LnFx3x
units.23
Hence, the linear variation observed in Fig. 1 is different.
According to eqn (6) it indicates that there is no long-lived
LixFy complex or KxFy complex: a fluoride anion surrounded
by a Li+ and b K+ gives a contribution to d equal to (a/a + b)
19F
dLiF + (b/a + b) 19FdKF. This result confirms the free
character of fluoride ions in molten alkali mixtures.
The F–Li+ and F–K+ radial distribution functions
extracted from MD simulations at various compositions and
a temperature of 1123 K are plotted on Fig. 2. The first peak of
these functions gives the structure of the solvation shell of
Fig. 1 Chemical shift of fluorine 19Fd as a function of the LiF molar
fraction in molten LiF–KF.
This journal is
c
the Owner Societies 2009
Fig. 2 F–Li and F–K radial distribution functions g(r) in molten
LiF–KF at various xLiF.
fluoride ions. It appears clearly that the position of the
maximum is nearly conserved: for all the mixtures the average
first neighbours distance shifts from 1.80 Å (xLiF = 0.1) to
1.83 Å (xLiF = 1) for F–Li and from 2.46 Å (xLiF = 0.0) to
2.53 Å (xLiF = 0.9) for F–K pairs. These distances are in very
good agreement with those experimentally obtained by X-ray
diffraction for the eutectic mixture24 (1.85 Å for F–Li) and are
very close to the similar molten fluoride system FLiNaK25
(1.83 Å for F–Li and 2.59 Å for F–K). The gradual shift of the
maximum with composition confirms the picture of a rapid
exchange between two limit environments corresponding to
the structure in the pure salts. These results are consistent with
the existence of LiFxK configuration (t = 0.3 ps) deduced
from Raman spectra26 but cannot be compared to the
complexes like those observed in YF3–AF mixtures for
examples.27,28 The maximum intensity of the first peak
decreases when xLiF increases for both Li–F and K–F pairs
(Fig. 2). This evolution is the signature of a decrease of
the association between the cations and the anions. Such a
phenomenon has already been evidenced in MD simulations
of the LiCl–KCl mixtures.29
Previous numerical simulations of this system have shown
the existence of local heterogeneities in ionic distribution, i.e.
clustering of Li+ and of part of the F ions in the KF
matrix.30,31 These effects do not affect the first solvation shell
because they correspond to the formation of medium range
order. Ribeiro has estimated a lifetime of a few picoseconds
for these clusters. It is therefore important to underline that
NMR of 19F nucleus is not able here to obtain direct evidence
Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11503
of such features since the residence time of ions in these
clusters is short compared to NMR characteristic time.
Concerning the other nuclei, the chemical shift range of 7Li
is too small to give evidence of a change in local structure and
the tuning range of our NMR probe does not cover the 39K
frequency.
3.2
Diffusion
3.2.1 Dependence on composition. The self-diffusion coefficients of fluorine DF, lithium DLi and potassium DK in molten
LiF–KF are plotted in Fig. 3 as a function of LiF molar
fraction xLiF at 10 K above the liquidus temperature and at
1123 K. They are also reported in Table 2. The whole set of
values obtained by HT PFG NMR and MD simulations are in
good agreement.
Fig. 3 Self-diffusion coefficient of fluorine DF, lithium DLi and
potassium DK as a function of LiF molar fraction xLiF: simulation
(full symbol) and experiment (open symbol) at 10 K above the liquidus
temperature (circle) and at 1123 K (square).
11504 | Phys. Chem. Chem. Phys., 2009, 11, 11501–11506
Table 2 Self-diffusion coefficients of fluorine DF, lithium DLi and
potassium DK in molten LiF–KF for various compositions and
temperatures
NMR
D 109
MD
NMR
MD
MD
xLiF T/K DF/m2 s1 DF/m2 s1 DLi/m2 s1 DLi/m2 s1 DK/m2 s1
0
0
0.1
0.1
0.2
0.2
0.3
0.3
0.3
0.4
0.4
0.4
0.45
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.7
0.7
0.7
0.7
0.8
0.8
0.9
0.9
1
1
1123
1173
1096
1123
1043
1123
973
1023
1123
887
1023
1123
833
775
817
858
906
954
1002
1037
1085
1123
773
873
1023
1123
1173
1200
877
1023
1123
961
1023
1123
1173
1033
1123
1083
1123
1123
1173
9.5
—
—
9.5
6.8
8.7
4.4
—
8.8
3.5
—
9.7
3.1
1.9
2.4
2.6
3.4
4.25
4.65
5.5
6.5
7.4
—
—
—
—
—
—
3.4
—
7.7
4.55
—
7.7
—
6.0
8.55
7.3
7.8
7.2
—
7.10
8.31
6.22
6.92
5.29
6.67
3.99
4.84
6.68
2.75
4.74
6.75
—
—
—
—
—
—
—
—
—
—
1.47
2.57
4.81
6.55
7.44
7.84
2.71
4.83
6.61
4.06
5.04
6.69
7.77
5.16
6.80
6.02
6.77
6.74
7.34
—
—
—
—
5.5
6.7
5
—
8.8
3.1
—
8.4
—
1.7
—
3.4
—
5.0
—
7.4
—
9.3
—
—
—
—
—
—
3.8
—
8.9
5
—
7.7
—
6.7
9
8.6
9.4
8.9
—
—
—
5.13
5.45
4.26
5.62
3.42
4.18
5.78
2.44
4.27
6.02
—
—
—
—
—
—
—
—
—
—
1.33
2.41
4.48
6.07
6.87
7.46
2.59
4.63
6.35
4.16
5.17
6.86
7.73
5.68
7.33
7.18
7.87
8.83
9.75
6.42
7.46
5.81
6.32
5.01
6.40
3.91
4.70
6.45
2.73
4.64
6.55
—
—
—
—
—
—
—
—
—
—
1.44
2.62
4.85
6.40
7.13
7.65
2.66
4.84
6.45
4.16
5.13
6.44
7.53
5.26
7.10
6.02
6.82
—
—
The striking point of this figure is that the dependence of
DF, DLi and DK on composition close to the liquidus
temperature mimics the LiF–KF phase diagram shape32 and
has been discussed in detail in a previous publication.10
Indeed, the self-diffusion coefficient strongly decreases from
pure KF to a minimum at the eutectic composition
(xLiF = 0.5) and increases again up to pure LiF. The amplitude
of this variation is considerable, as the values range from
2 109 to 9 109 m2 s1, spanning almost one order of
magnitude. In many liquids, the composition strongly affects
the dynamic properties in general and the self-diffusion
coefficient in particular. This is for example the case for
molten LiF–BeF2 mixtures for which all diffusion coefficients
strongly decrease with increasing BeF2 concentration33
(data supplied in the ESI).w In contrast, the self-diffusion
coefficients of anions and cations are here only weakly affected
by the Li/K ratio, the temperature effect is much stronger.
This is confirmed by the values of DF, DLi and DK determined
This journal is
c
the Owner Societies 2009
for each composition at 1123 K which lie on straight
lines (Fig. 3) between the limiting values for the pure
fluids.
Some discrepancies are observed between the results
obtained in the MD simulations and HT PFG NMR on the
KF rich side. This mainly occurs in the case of lithium ions
where the MD simulations underestimate the diffusion
coefficients of F and Li+. This may be related to the inherent
uncertainties of both techniques applied to molten fluorides
especially the accuracy of the interaction potential used in the
MD simulations and the accuracy of setting the temperature in
HT PFG NMR. Complementary work using other techniques
like electrochemical experiments should help in refining the
whole set of data. Such techniques have already allowed the
determination of the self-diffusion coefficients of electroactive species. For example, it was shown that DZr equals
2.9 109 m2 s1 at 1020 K in molten LiF–NaF–ZrF434 and
that DGd increases from 1.25 109 m2 s1 to 2.6 109 m2 s1
for temperatures of 1073 to 1173 K in molten LiF–CaF2.35
The influence of the composition has already been studied in
LiCl–KCl and in LiNO3–KNO3 by MD simulations28,36 has
been compared to experimental data.37,38 Going from pure
lithium compound to pure potassium compound a substantial
decrease of the self-diffusion coefficients was observed for all
species.
In LiCl–KCl at 1096 K this effect was more pronounced
for DLi (about 50%) than for DK (about 40%) and DCl
(about 20%). At much lower temperature (575 K) in
LiNO3–KNO3 the same trend occurs: DLi (about 60%),
DK (about 50%) and DNO3 (about 50%). The comparison
between fluoride, chloride and nitrate systems indicates the
importance of the size and polarizability of the anion on the
diffusive properties of all species. The larger the anion and
the greater its polarizability, the greater the composition
dependence.
3.2.2 Activation energy of diffusion. The activation
energies, Ea, for diffusion have been determined for the three
ions at the eutectic composition (xLiF = 0.5). The temperature
was scanned from 773 to 1123 K for HT PFG NMR
measurements and from 773 to 1200 K for the MD simulations.
The logarithm of the diffusion coefficients is plotted in Fig. 4
as function of 1/RT (R is the ideal gas constant). The activation
energy obtained by linear regressions on the straight lines in
Fig. 4 is reported in Table 3.
These values are in very close agreement with the experimental data obtained using the capillary method on similar
systems:39 in molten NaF Ea = 36.0 kJ mol1 for Na+.
In contrast, the activation energies in a network-like molten
fluoride salts LiBeF2 are much greater32: 76 kJ mol1 for Be2+
and F, 54 kJ mol1 for Li+.
Table 3
Fig. 4 Ln(DF), Ln(DLi) and Ln(DK) versus 1/RT in molten LiF–KF
(xLiF = 0.5). Lines are the results of the linear regressions.
It is known that Ea increases with the solvation cage
stability, in other words, with the strength of the interaction
between cation and anion. This suggests that an activation
energy around 30 kJ mol1 is the signature of free species in
molten fluorides.
Activation energy of diffusion
Methods
Ea(Li+) kJ mol1
Ea(K+) kJ mol1
Ea(F) kJ mol1
MD simulations
HT PFG NMR
30.1
33.0
28.5
29.7
27.9
This journal is
c
the Owner Societies 2009
Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11505
Conclusions
We have studied the diffusive properties in molten LiF–KF
mixtures over a wide range of composition and temperature.
An overall good agreement is obtained between experiments
(HT PFG NMR) and theory (MD simulations) which confirms
the reliability of our results. We showed that, unlike the
analogous chloride (LiCl–KCl) and nitrate (LiNO3–KNO3)
systems, the composition affects the diffusive properties only
weakly. The self-diffusion coefficient varies mainly with
temperature. In addition, the activation energy reveals the
bonding character of a given ion in the molten salt.
Acknowledgements
The authors are indebted to Frank Engelke, Ernst Naumann
and Klaus Zick from Bruker Co. for the NMR probe. The
authors thank NMR group members of CEMHTI for
valuable discussions, in particular F. Fayon. The authors are
grateful to Eric Labrude for his technical help. This work has
been supported by GdR PARIS and by PCR ANSF of
programme PACEN.
References
1 M. Rovere and M. P. Tosi, Rep. Prog. Phys., 1986, 49, 1001.
2 A. Nuttin, D. Heuer, A. Billebaud, R. Brissot, C. Le Brun,
E. Liatard, J. M. Loiseaux, L. Mathieu, O. Meplan, E. MerleLucotte, H. Nifenecker, F. Perdu and S. David, Prog. Nucl.
Energy, 2005, 46, 77.
3 L. Mathieu, D. Heuer, R. Brissot, C. Garzenne, C. Le Brun,
D. Lecarpentier, E. Liatard, J. M. Loiseaux, O. Meplan,
E. Merle-Lucotte, A. Nuttin, E. Walle and J. Wilson, Prog. Nucl.
Energy, 2006, 48, 664.
4 O. Beneš and R. J. M. Konings, CALPHAD: Comput. Coupling
Phase Diagrams Thermochem., 2008, 32, 121.
5 E. Renaud, C. Robelin, M. Heyrman and P. Chartrand, J. Chem.
Thermodyn., 2009, 41, 666.
6 V. Dracopoulos, B. Gilbert and G. N. Papatheodorou, J. Chem.
Soc., Faraday Trans., 1998, 94, 2601.
7 F. Auguste, O. Tkatcheva, H. Mediaas, T. Ostvold and B. Gilbert,
Inorg. Chem., 2003, 42, 6338.
8 B. Tremillion, in Acid–base effects in molten electrolytes, molten
salts chemistry, ed. Mamantov and Marassi, Dordrecht, NATO
ASI series, Series C, 1987, vol. 202, pp. 279–309.
9 G. J. Janz, F. W. Dampier, G. R. Lakshminarayanan,
P. K. Lorenz and R. P. T. Tomkins, National Standard Reference
Data Series, Molten Salts: Volume 1. Electrical Conductance,
Density, and Viscosity Data, 1968, vol. 15.
10 A.-L. Rollet, V. Sarou-Kanian and C. Bessada, Inorg. Chem,
in press.
11506 | Phys. Chem. Chem. Phys., 2009, 11, 11501–11506
11 C. S. Johnson, Jr., Prog. Nucl. Magn. Reson. Spectrosc., 1999, 34,
203.
12 P. A. Madden, R. Heaton, A. Aguado and S. Jahn, THEOCHEM,
2006, 771, 9.
13 A.-L. Rollet, V. Sarou-Kanian and C. Bessada, C. R. Chimie,
submitted.
14 R. M. Cotts, M. J. R. Hoch, T. Sun and J. T. Markert, J. Magn.
Reson., 1989, 83, 252.
15 R. Heaton, R. Brookes, P. Madden, M. Salanne, C. Simon and
P. Turq, J. Phys. Chem. B, 2006, 110, 11454.
16 G. J. Martyna, D. Tobias and M. L. Klein, J. Chem. Phys., 1994,
101, 4177.
17 H. Fukui, Prog. Nucl. Magn. Reson. Spectrosc., 1997, 31, 317.
18 V. Lacassagne, C. Bessada, P. Florian, S. Bouvet, B. Ollivier,
J.-P. Coutures and D. Massiot, J. Phys. Chem. B, 2002, 106,
1862.
19 A.-L. Rollet, C. Bessada, A. Rakhmatullin, Y. Auger, P.
Melin, M. Gailhanou and D. Thiaudière, C.R. Chimie, 2004, 7,
1135.
20 C. Bessada, A.-L. Rollet, A. Rakhmatullin, I. Nuta, P. Florian and
D. Massiot, C.R. Chimie, 2006, 9, 374.
21 C. Bessada, A. Rakhmatullin and A.-L. Rollet, J. Nucl. Mater.,
2007, 360, 43.
22 The lifetimes of these units are about the picoseconds that is much
shorter than the NMR characteristic time.
23 A.-L. Rollet, S. Godier and C. Bessada, Phys. Chem. Chem. Phys.,
2008, 10, 3222.
24 K. Igarashi, M. Murofushi, Y. Iwadate, J. Mochinaga and
H. Ohno, Chem. Lett., 1985, 817.
25 K. Igarashi, Y. Okamoto, J. Mochinaga and H. Ohno, J. Chem.
Soc., Faraday Trans. 1, 1988, 84, 4407.
26 V. Dracopoulos and G. N. Papatheodorou, Phys. Chem. Chem.
Phys., 2000, 2, 2021.
27 V. Dracopoulos, B. Gilbert, B. Borensen, G. M. Photiadis and
G. N. Papatheodorou, J. Chem. Soc., Faraday Trans., 1997, 93,
3081.
28 C. Bessada, A. Rakhmatullin, A.-L. Rollet and D. Zanghi,
J. Fluorine Chem., 2009, 130, 45–42.
29 B. Morgan and P. A. Madden, J. Chem. Phys., 2004, 120, 1402.
30 M. C. Ribeiro, J. Phys. Chem. B, 2003, 107, 4392.
31 M. Salanne, C. Simon, P. Turq and P. A. Madden, J. Phys.:
Condens. Matter, 2008, 20, 332101.
32 J. Sangster and A. D. Pelton, J. Phys. Chem. Ref. Data, 1987, 16,
509.
33 M. Salanne, C. Simon, P. Turq and P. A. Madden, J. Phys. Chem.
B, 2007, 111, 4678.
34 H. Groult, A. Barhoun, H. El Ghallali, S. Borensztjan and
F. Lantelme, J. Electrochem. Soc., 2008, 155, E19.
35 C. Nourry, L. Massot, P. Chamelot and P. Taxil, Electrochim.
Acta, 2008, 53, 2650.
36 M. C. Ribeiro, J. Chem. Phys., 2002, 117, 266.
37 R. Lenke, W. Uebelhack and A. Klemm, Z. Naturforsch. A, 1973,
28, 881.
38 G. J. Janz and N. P. Bansal, J. Phys. Chem. Ref. Data, 1982, 11,
505.
39 D. Harari, F. Lantelme and M. Chemla, C. R. Acad. Sci. II C,
1970, 270C, 653.
This journal is
c
the Owner Societies 2009