Journal of New Materials for Electrochemical Systems 9, 291-295 (2006)
© J. New. Mat. Electrochem. Systems
Molecular Dynamics Simulation of Hydrogen Fluoride Mixtures with
1-Ethyl-3-Methylimidazolium Fluoride: Dynamic Features
M. Salanne, ∗ C. Simon and P. Turq
Université Pierre et Marie Curie-Parisn 6, CNRS, ESPCI, UMR 7612, laboratoire LI2C,
case courier 51, 4 place Jussieu, 75252 Paris Cedex 05, France
Received: March 01, 2006, Accepted: April 25, 2006
Abstract: Imidazolium fluoride and hydrogen fluoride mixtures are interesting intermediate systems having features of room
temperature ionic liquids (RTIL), hydrogen-bonded molecular liquids, and molten salts. Furthermore, they could be used in a wide
variety of electrochemical applications, as media for fluorine generation, as solvent for organic chemistry or as electrolytes in
batteries or fuel cells.
It is possible to model these mixtures with classical interaction potentials known to describe well HF, and combination of LennardJones potentials for the molecular cations. Molecular Dynamics simulations (MD) have been conducted to investigate both structural
and transport properties of these mixtures. In this paper, the values of the self-diffusion coefficients are especially commented, and
compared with experimental results. Impact of structure of the first solvation shell on the dynamics properties of the ions is also
depicted.
Keywords: Room temperature ionic liquids, Polyfluoride anions, Molecular dynamics, Diffusion coefficients
These features have been attributed to the formation
of so-called polyfluoride anions, which are formed of a
central fluoride anion surrounded by one or several HF
molecules. Evidence for the existence of these species was
given by IR spectroscopy [6]. Hagiwara et al. observed
unambiguously the formation of the bifluoride F(HF)− ,
μ-fluoro-bis(fluorohydrogenate) F(HF)2 − and μ3 -fluorotris(fluorohydrogenate) F(HF) 3 − ions. The general topology of those three anions is shown on figure 1. Our previous simulation results [7] agreed with such a speciation
and we found that in EMIF-2.3HF the percentage of those
3 species were respectively of 10%, 40% and 50%. In their
ab initio molecular dynamics study of KF-2HF, Klein et al.
also obtained more complicated ions [8]. Unfortunately, IR
spectroscopy is not sufficient to confirm or dismiss the existence of these later species. NMR experiments carried out
on those liquids only showed one signal for either fluorine
or hydrogen atoms because the exchange of HF molecules
is fast compared to the NMR time resolution.
The importance of the polyfluoride species in those liquids can be illustrated in writing the reactions involved in
the use of EMIF-2.3HF as an electrolyte in a fuel cell:
1. INTRODUCTION
Mixtures of fluorinated ionic liquids with hydrogen fluoride (HF) have always raised huge interest in the field
of electrochemistry. Among them, the melt KF-2HF is
the key system for the production of fluorine through electrolysis [1,2]. Recently the interest in room temperature
ionic liquids (RTIL) has severely increased, and mixtures of
RTIL with HF were synthetized [3]. Although they were
not tested in an industrial sized process, many applications of these liquids, and particularly of the 1-ethyl-3methylimidazolium fluoride mixture with 2.3 equivalents
of HF (EMIF-2.3HF), can be previewed. For example,
Hagiwara et al. showed that such liquids could be advantageously used as electrolytes in fuel cells. Their physicochemical properties [4] are indeed very interesting: EMIF2.3HF has a conductivity of 100 mS.cm−1 and a viscosity
of 4.85 cP at 298K,whereas in “normal” RTILs (i.e. not
mixed with HF) σ and η are respectively of the order of
13.5 mS.cm−1 and 31.8 cP (these values correspond to the
1-ethyl-3-methylimidazolium tetrafluoroborate) at such a
temperature [5].
∗ To
whom corresponding to: E-mail: [email protected]; Phone:
+33144273265; Fax: +33144273228
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M. Salanne et al. / J. New Mat. Electrochem. Systems
Table 1. Simulation parameters
a (angstroms)
b (angstroms)
c (angstroms)
Temperatures
System 1 System 2 System 3 System 4
37.0331 37.0331 37.0331 37.0331
32.1957 32.4866 32.9702 33.2856
41.7108 41.7108 41.7108 41.7108
298 K
320 K
340 K
353 K
cal=4.184 J) and distances in angstroms):
Figure 1. Typical conformation of the polyfluorides (Black:
Fluorine atoms, white: Hydrogen atoms). These represent only instantaneous geometry, and not averaged or
most probable geometry. Ions undergo constantly streching, bending, torsions and vibrations. It would be spurious
to deduce symmetry of the ions in the liquid on the single
basis of these snapshots.
Anode: H2 +8F(HF)2
−
−
→ 6F(HF)3 +2e−
−
−
Cathode: 1/2O2 +6F(HF)3 +2e− → H2 O+8F(HF)2
The liquid at composition EMIF-1.3HF can also be used
in such an application. In that case the reactions would
involve the F(HF)− and F(HF)2 − anions.
On the basis of molecular dynamics, deep insight of the
speciation could help understanding and modeling kinetics
of those processes, and could contribute to the optimization efforts of those electrolytes regarding each specific application. Furthermore molecular dynamics can provide a
picture of the diffusion of the species in those liquids, which
is also necessary.
2. MODEL AND METHODS
2.1. Interaction potentials
We chose the so-called HF3 model developed by Klein
et al. for the HF molecules [9]. This model is a three
site description and the bond length is 0.9118 Angstroms.
Both the hydrogen and fluorine atom carry a charge of
+0.68 e and a compensating charge of —1.36 e is placed
between them on the molecule axis, at a distance of 0.165
Angstroms from the fluorine ion. The molecules are kept
rigid, and the non-Coulombic terms of the intermolecular
potential between two of them are of the following form
(where all the potentials are expressed in kcal.mol−1 (1
VF F (r) = 2 × 105 exp(−4.25r) − V Disp (r)
(1)
V Disp (r) = f (r)(220/r6 + 400/r8 + 4500/r10 )
(2)
f (r) = exp(−(4.7/r − 1)2 ) if r ≤ 4.7
= 1 else
(3)
VF H (r) = 2[exp(−10.6(r − 1.6)) − 2 exp(−5.3(r − 1.6))] (4)
VHH (r) = 600 exp(−3.34r)
(5)
To model 1-ethyl-3-methylimidazolium molecules, we used
the AMBER force field [10] developed by Cornell et al. In
this representation, the potential energy takes the following
form:
X
X
Vtotal =
Kr (r − req )2 +
Kθ (θ − θeq )2
bonds
angles
X
+
Vn /2[1 + cos(nϕ − γ)]
Xdihedrals
12
6
+
[Aij /rij
− Bij /rij
+ qi qj /rij ]
(6)
i<j
All the values used for the various parameters are given
in reference [7]; they were mostly taken from a previous study on 1-ethyl-3-methylimidazolium tetrachloroaluminate by de Andrade et al [11]. This combination of
potentials appeared to provide excellent description of the
structural properties of the liquid [7].
2.2. Computational details
The MD simulations were performed using DLPOLY
[12], version 2.14. The Verlet algorithm was used with a
timestep of 1 fs to integrate the equations of motion. The
system was studied at four different temperatures: 298K,
320K, 340K and 353K. The simulation cell shapes are specified in table 1. The boxes contained 192 EMIF pairs and
440 HF molecules, yielding a HF/EMIF ratio of 2.3 and a
total of 5160 atoms. In all cases the density is set to the
experimental one [4]. In all runs the pressure fluctuated
between 0 and 1 kbar. Five successive 200 ps simulations
at increasing temperatures, starting at 2 K, were used to
thermalize the system before to perform a 1 ns simulation
in the microcanonical ensemble. A cut-off radius of 16
Angstroms was used for the calculation of the short-range
interactions, while the long-range electrostatic interactions
were treated using the Ewald summation method [13].
Molecular Dynamics Simulation of Hydrogen Fluoride Mixtures with 1-Ethyl
-3-Methylimidazolium Fluoride: Dynamic Features / J. New Mat. Electrochem. Systems
Figure 2. Mean square displacements of the hydrogen
atoms belonging to the cations, as a function of time,at
4 temperatures: 353 K (top curve), 340 K, 320 K and 298
K (bottom curve).The slope of the linear part (t > 75 ps)
is proportional to 6 times the self-diffusion coefficient.
293
Figure 3. Arrhenius plots of the self-diffusion coefficients
obtained from simulations for hydrogen and fluoride atoms.
The activation energies are deduced from the slopes.
Table 2. Activation energies (kJ.mol−1 )
3. RESULTS AND DISCUSSION
3.1. Self-diffusion coefficients of cations and anions
Hagiwara et al. have used the pulsed gradient spin-echo
NMR technique to measure self-diffusion coefficients [14].
In order to compare our results to the experimental ones,
we calculated the diffusion coefficients of hydrogen atoms
in the cations and of both the hydrogen and fluorine atoms
in the anions. For each temperature, we computed the
mean-square displacement (MSD) of each of these species
over the full trajectory. The diffusion coefficients are then
obtained by plotting the MSD versus time, as shown for
the hydrogen atoms of the cations at the various studied
temperature on figure 2: the slope of the linear part of the
curve is then equal to 6 D.
The values obtained for the diffusion coefficients are
shown on figure 3: They are roughly one order of magnitude smaller than the experimental ones. However, this
difference may be attributed to the model used for the
1-ethyl-3-methylimidazolium cations: in other simulation
studies using this model the same kind of deviations from
experiments can be observed: calculated diffusion coefficients are generally smaller than the experimental ones.
Voth et al. showed that using an electronically polarizable
model improved the agreement between experiment and
simulation[15]. But, to our knowledge, our study yields
the higher values obtained by simulation for an ionic liquid
at room temperature. This is consistent with experiments
since EMIF-2.3HF has one of the lowest viscosities and of
the highest conductivities and diffusion coefficients of this
class of products.
To go beyond this qualitative agreement between our
simulations and experiments, the arrhenian behavior of the
Experiments[14]
Simulation
H cation
16.4
18.4
H anion
16.2
17.2
F anion
14.7
15
system was examined. Plotting log D versus 1/T , we obtained straight lines, allowing determination of activation
energies Ea with the relationship:
D = D0 exp(−Ea /RT )
(7)
Our results for the various atom studied are given in table 2, to be compared with experimental ones. The agreement is excellent, suggesting that the problem with our
diffusion coefficients comes from D0 in the previous equation.
3.2. Separating the contribution from the various
polyfluorides
An advantage of the molecular dynamics simulations is
their atomic scale that allows distinguishing the various
contributions to observable quantities. For the present system, we can for example calculate the diffusion coefficients
of the different polyfluoride anions. An HF molecule is
considered bonded to a given fluoride ion if the distance
between the hydrogen atom and the fluoride ion is smaller
than a cutoff value of 2.1 angstroms. The choice of this criterion is fully discussed in reference [16]. Experimentally,
the exchange of HF molecules between two polyfluorides is
very fast compared to the NMR timescale and thus their
individual contributions cannot be determined.
The Arrhenius plots of the diffusion coefficients of the
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M. Salanne et al. / J. New Mat. Electrochem. Systems
Figure 4. Arrhenius plots of the self-diffusion coefficients
of the various polyfluorides. At all temperatures, selfdiffusion of higher weight ions is faster than the one of
lighter ions.
various anions are given on figure 4. It appears that they
increase with the number of HF molecules in the cluster: at
all the studied temperatures, D(F(HF)3 − ) > D(F(HF)2 − )
> D(F(HF)− ). While surprising, this result is consistent
with conductivity results obtained by Hagiwara et al [6].
These authors indeed studied the influence of the HF fraction x (with 1.0 < x < 2.6) in EMIF-xHF and showed
that the conductivity increases with x. The diffusion coefficients can be related to the electrical conductivity by the
Nernst-Einstein equation:
X
σ N E = βe2
ρi qi Di
(8)
where ρi , qi and Di are respectively the number density,
charge and diffusion coefficient of species i. In the EMIFxHF melt, the increase of x is associated with an increase
of the proportion of F(HF)3 − ions. The higher diffusion
coefficient of this species is then sufficient to explain the
rise of the electrical conductivity of the liquid.
3.3. Coupling the diffusion to the liquid structure
The later result can be surprising as the size of the
anion of course increases with the number of HF molecules bonded to the central fluoride anion. One would be
tempted to think that a smaller molecule would diffuse easier. Such results are obtained in high temperature molten
salts. For example, Madden et al. showed that in the
LiCl/KCl eutectic [17], La3+ or Y3+ cations diffuse much
slower than the smaller Li+ and K+ . But in such liquids,
the smaller mobility of big cations is due to their high coordination number: they diffuse with an intact coordination
shell whereas smaller ions diffuse as isolated spherical particles. Thus we calculated the coordination numbers of the
3 varieties of anions present in our system; the results are
summarized in figure 5.
Figure 5. Percentage of anions with a given coordination
number (i.e. number of cation surrounding a given anion).
F(HF)- is surrounded by a higher number of cations (its
most probable coordination numbers are 3, and then 4)
than F(HF)3 - (whose most probable coordination number
is only 2).
The coordination number decreases when passing from
F(HF)− to F(HF)3 − , which is coherent with the screening
of the central charge by the HF molecules in the later.
The most probable coordination numbers are then 3 to 4
for F(HF)− and 1 to 2 for F(HF)3 − . It is then clear that
the later can diffuse more easily, whereas the F(HF)− ions
rattle in a cage of imidazolium cations.
4. CONCLUSION
In a previous study, we have shown that our model provided excellent structural results, matching very well Xray diffraction experimental results. In the present paper,
we have furthermore demonstrated that the model is in
qualitative agreement with experiments regarding transport properties, namely self-diffusion coefficients. Quantitative agreement is also obtained for activation energies.
The molecular details provided by the simulation allow
deeper insight to the contributions of the various species
present in the liquid: it is even possible to relate the selfdiffusion coefficients of each polyfluoride ion with their environment. F(HF)3 − , which is the anion containing the
more HF molecules, is counter-intuitively the more mobile species: This is due to its smaller coordination number. This latest feature also explains the experimentally
observed increase of conductivity with the HF proportion
in EMIF-xHF.
5. ACKNOWLEDGEMENT
The authors would like to thank professor Rika Hagiwara
for fruitful discussions.
Molecular Dynamics Simulation of Hydrogen Fluoride Mixtures with 1-Ethyl
-3-Methylimidazolium Fluoride: Dynamic Features / J. New Mat. Electrochem. Systems
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